prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Quantum Mechanics - I
The Unmaking of Classical Physics
RISHIKESH VAIDYA
rishidilip@gmail.com
Physics Department, BITS-Pilani, Pilani.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Anyone who is not shocked by
quantum theory has not
understood it.
Neils Bohr
The converse is of course not
true. Don’t let your grades
prove to you.
Rishikesh Vaidya
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Anyone who is not shocked by
quantum theory has not
understood it.
Neils Bohr
The converse is of course not
true. Don’t let your grades
prove to you.
Rishikesh Vaidya
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Outline
1
prelude
2
Course Structure
3
Quantum Shock
4
Being Photon
A twist in the spin
5
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
The place of quantum theory in overall scheme of
things
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
The place of quantum theory in overall scheme of
things
Shaunak’s question to Angiras (Mundaka Upnishad 1.1.3)
Sir, what is it knowing which, everything else becomes known?
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
The place of quantum theory in overall scheme of
things
Shaunak’s question to Angiras (Mundaka Upnishad 1.1.3)
Sir, what is it knowing which, everything else becomes known?
I would like to view this question from a reductionist
perspective. It admits the existence of elementary conceptual
building blocks to(from) which complex reality can be
de(re)constructed. Quantum theory is then this science of
ultimate reduction (as of today!).
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Quantum Mechanics is different!
Classical physics is beautiful. It is –
Fairly simple (taught in schools)
Economical (governed by few simple laws)
Explains most of the palpable phenomena that we can see
(Mechanics, Optics, electrodynamics), hear (sAcoustics)
and feel (thermodynamics)
Confers to our classica reasoning and logic (this will be
soon qualified and quantified!)
Relativity is surely crazy, only as long as you do not
understand it. Makes immense sense once you get the
hang of it.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Quantum Mechanics is different!
Classical physics is beautiful. It is –
Fairly simple (taught in schools)
Economical (governed by few simple laws)
Explains most of the palpable phenomena that we can see
(Mechanics, Optics, electrodynamics), hear (sAcoustics)
and feel (thermodynamics)
Confers to our classica reasoning and logic (this will be
soon qualified and quantified!)
Relativity is surely crazy, only as long as you do not
understand it. Makes immense sense once you get the
hang of it.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Quantum Mechanics is different!
Classical physics is beautiful. It is –
Fairly simple (taught in schools)
Economical (governed by few simple laws)
Explains most of the palpable phenomena that we can see
(Mechanics, Optics, electrodynamics), hear (sAcoustics)
and feel (thermodynamics)
Confers to our classica reasoning and logic (this will be
soon qualified and quantified!)
Relativity is surely crazy, only as long as you do not
understand it. Makes immense sense once you get the
hang of it.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Quantum Mechanics is different!
Classical physics is beautiful. It is –
Fairly simple (taught in schools)
Economical (governed by few simple laws)
Explains most of the palpable phenomena that we can see
(Mechanics, Optics, electrodynamics), hear (sAcoustics)
and feel (thermodynamics)
Confers to our classica reasoning and logic (this will be
soon qualified and quantified!)
Relativity is surely crazy, only as long as you do not
understand it. Makes immense sense once you get the
hang of it.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Quantum Mechanics is different!
Classical physics is beautiful. It is –
Fairly simple (taught in schools)
Economical (governed by few simple laws)
Explains most of the palpable phenomena that we can see
(Mechanics, Optics, electrodynamics), hear (sAcoustics)
and feel (thermodynamics)
Confers to our classica reasoning and logic (this will be
soon qualified and quantified!)
Relativity is surely crazy, only as long as you do not
understand it. Makes immense sense once you get the
hang of it.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Quantum Mechanics is different!
Quantum Mechanics is truly bizarre!
You cannot come to understand quantum mechanics in a way
you make sense of classical physics and Relativity. It not only
refuses to answer our naively classical questions, it audaciously
redefines what we can ask and what we cannot. Not only that,
it challenges our naive classical reasoning and logic.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
QM-1 is different as a course as well!
Newtonian Mechanics was, not surprisingly, developed
single handedly by Newton. Its principles can be written
down on a sheet paper and has far less ‘structure’ to it.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
QM-1 is different as a course as well!
Analytical Mechanics was developed mainly D’Alembert,
Lagrange, Hamilton, and Jacobi. Although it is equivalent
to Newtonian mechanics, it has far more structure to it and
hence is very powerful and versatile in its application.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
QM-1 is different as a course as well!
The structural aspects of Quantum Mechanics cannot be
divorced from the structural aspects of classical
mechanics, electrodynamics, thermodynamics, and
statistical mechanics as it has to reproduce them in
appropriate limits. Yet the whole (QM) is radically different
from the summation of the parts. It was developed over a
period of 3 decades with fundamental contributions from
over 2 dozen physicists. The point is, you cannot do
problems in quantum mechanics without a deeper
understanding of its structural aspects, unlike Newtonian
mechanics which is a straight forward application of its
principles.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
So what’s the fuss all about?
Quantum mechanics pulls the rug from under the most
cherished notions through which we make sense of the
physical reality around us. It trades
exclusive identity with wave-particle dualism
determinism with uncertainty and probability
objectivity with subjectivity (caution !)
continuum with discrete Quantum
Any one of this attribute in itself is bizzare enough. Put together
it is outlandish, outragious, queer, and weird! How are we
supposed to make sense of all this?
Or perhaps, mother nature may accurately describe us with just
one adjective – pretentious!
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
So what’s the fuss all about?
Quantum mechanics pulls the rug from under the most
cherished notions through which we make sense of the
physical reality around us. It trades
exclusive identity with wave-particle dualism
determinism with uncertainty and probability
objectivity with subjectivity (caution !)
continuum with discrete Quantum
Any one of this attribute in itself is bizzare enough. Put together
it is outlandish, outragious, queer, and weird! How are we
supposed to make sense of all this?
Or perhaps, mother nature may accurately describe us with just
one adjective – pretentious!
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
So what’s the fuss all about?
Quantum mechanics pulls the rug from under the most
cherished notions through which we make sense of the
physical reality around us. It trades
exclusive identity with wave-particle dualism
determinism with uncertainty and probability
objectivity with subjectivity (caution !)
continuum with discrete Quantum
Any one of this attribute in itself is bizzare enough. Put together
it is outlandish, outragious, queer, and weird! How are we
supposed to make sense of all this?
Or perhaps, mother nature may accurately describe us with just
one adjective – pretentious!
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
So what’s the fuss all about?
Quantum mechanics pulls the rug from under the most
cherished notions through which we make sense of the
physical reality around us. It trades
exclusive identity with wave-particle dualism
determinism with uncertainty and probability
objectivity with subjectivity (caution !)
continuum with discrete Quantum
Any one of this attribute in itself is bizzare enough. Put together
it is outlandish, outragious, queer, and weird! How are we
supposed to make sense of all this?
Or perhaps, mother nature may accurately describe us with just
one adjective – pretentious!
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
So what’s the fuss all about?
Quantum mechanics pulls the rug from under the most
cherished notions through which we make sense of the
physical reality around us. It trades
exclusive identity with wave-particle dualism
determinism with uncertainty and probability
objectivity with subjectivity (caution !)
continuum with discrete Quantum
Any one of this attribute in itself is bizzare enough. Put together
it is outlandish, outragious, queer, and weird! How are we
supposed to make sense of all this?
Or perhaps, mother nature may accurately describe us with just
one adjective – pretentious!
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
So what’s the fuss all about?
Quantum mechanics pulls the rug from under the most
cherished notions through which we make sense of the
physical reality around us. It trades
exclusive identity with wave-particle dualism
determinism with uncertainty and probability
objectivity with subjectivity (caution !)
continuum with discrete Quantum
Any one of this attribute in itself is bizzare enough. Put together
it is outlandish, outragious, queer, and weird! How are we
supposed to make sense of all this?
Or perhaps, mother nature may accurately describe us with just
one adjective – pretentious!
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
So what’s the fuss all about?
Quantum mechanics pulls the rug from under the most
cherished notions through which we make sense of the
physical reality around us. It trades
exclusive identity with wave-particle dualism
determinism with uncertainty and probability
objectivity with subjectivity (caution !)
continuum with discrete Quantum
Any one of this attribute in itself is bizzare enough. Put together
it is outlandish, outragious, queer, and weird! How are we
supposed to make sense of all this?
Or perhaps, mother nature may accurately describe us with just
one adjective – pretentious!
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
The Course and the Evaluation
Books:
Quantum Mechanics by Bransden and Joachain, Pearson
Quantum Mechanics Vo. 1 Shin-itiro Tomonaga
Quantum Mechanics by Powell and Crasseman Narosa
Quantum Mechanics by David Bohm Dover
The course structure in brief
Inevitability of the birth of QM ( 10 lectures, Tomonaga
Chap. 1,2, Chap.1 BJ)
Rudiments of Schrodinger’s wave mechanics ( 16 lectures,
Chap.2,3 BJ)
Applications to simple 1-dimensional systems ( 7 lectures,
Chap.4 BJ)
Rudiments of the formal structure of QM ( 7 Lecture, Sec.
5.1-5.4, BJ)
Evaluation components: Tutorials (Best 10 from 13, 27 %),
Midsem (30 %),Rishikesh
Comprehensive
( 43 %)
Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
The Course and the Evaluation
Books:
Quantum Mechanics by Bransden and Joachain, Pearson
Quantum Mechanics Vo. 1 Shin-itiro Tomonaga
Quantum Mechanics by Powell and Crasseman Narosa
Quantum Mechanics by David Bohm Dover
The course structure in brief
Inevitability of the birth of QM ( 10 lectures, Tomonaga
Chap. 1,2, Chap.1 BJ)
Rudiments of Schrodinger’s wave mechanics ( 16 lectures,
Chap.2,3 BJ)
Applications to simple 1-dimensional systems ( 7 lectures,
Chap.4 BJ)
Rudiments of the formal structure of QM ( 7 Lecture, Sec.
5.1-5.4, BJ)
Evaluation components: Tutorials (Best 10 from 13, 27 %),
Midsem (30 %),Rishikesh
Comprehensive
( 43 %)
Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
The Course and the Evaluation
Books:
Quantum Mechanics by Bransden and Joachain, Pearson
Quantum Mechanics Vo. 1 Shin-itiro Tomonaga
Quantum Mechanics by Powell and Crasseman Narosa
Quantum Mechanics by David Bohm Dover
The course structure in brief
Inevitability of the birth of QM ( 10 lectures, Tomonaga
Chap. 1,2, Chap.1 BJ)
Rudiments of Schrodinger’s wave mechanics ( 16 lectures,
Chap.2,3 BJ)
Applications to simple 1-dimensional systems ( 7 lectures,
Chap.4 BJ)
Rudiments of the formal structure of QM ( 7 Lecture, Sec.
5.1-5.4, BJ)
Evaluation components: Tutorials (Best 10 from 13, 27 %),
Midsem (30 %),Rishikesh
Comprehensive
( 43 %)
Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Waves OR Particles: Cracking the electron identity
Particle: Localized bundles of energy and momentum,
described by q(t), q̇(t) (or q(t), p(t)), evolve according to 2nd
order equations of motion.
Wave: A disturbance spread over space and time, described by
a wave-function ψ(~r , t) which characterizes the disturbance at
the point ~r at a time t. Time evolution described by 2nd order
wave equation.
However, Waves are waves and particles are particles !
But we need operational definitions that would stand against
the results of some experiment.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Waves OR Particles: Cracking the electron identity
Particle: Localized bundles of energy and momentum,
described by q(t), q̇(t) (or q(t), p(t)), evolve according to 2nd
order equations of motion.
Wave: A disturbance spread over space and time, described by
a wave-function ψ(~r , t) which characterizes the disturbance at
the point ~r at a time t. Time evolution described by 2nd order
wave equation.
However, Waves are waves and particles are particles !
But we need operational definitions that would stand against
the results of some experiment.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Waves OR Particles: Cracking the electron identity
Particle: Localized bundles of energy and momentum,
described by q(t), q̇(t) (or q(t), p(t)), evolve according to 2nd
order equations of motion.
Wave: A disturbance spread over space and time, described by
a wave-function ψ(~r , t) which characterizes the disturbance at
the point ~r at a time t. Time evolution described by 2nd order
wave equation.
However, Waves are waves and particles are particles !
But we need operational definitions that would stand against
the results of some experiment.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A Double Slit Experiment with Bullets
Imagine a Drunkard spraying bullets with a Gun randomly in all
directions.
(All images in this section from: http://www.upscale.utoronto.ca/PVB/Harrison/DoubleSlit/DoubleSlit.html)
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A Double Slit Experiment with Bullets
Imagine a Drunkard spraying bullets with a Gun randomly in all
directions.
(All images in this section from: http://www.upscale.utoronto.ca/PVB/Harrison/DoubleSlit/DoubleSlit.html)
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A Double Slit Experiment with Bullets
Imagine a Drunkard spraying bullets with a Gun randomly in all
directions.
(All images in this section from: http://www.upscale.utoronto.ca/PVB/Harrison/DoubleSlit/DoubleSlit.html)
Slit 1 open:
What we can
measure is the
probability P1 of
finding a bullet a
distance x from
the center.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A Double Slit Experiment with Bullets
Imagine a Drunkard spraying bullets with a Gun randomly in all
directions.
(All images in this section from: http://www.upscale.utoronto.ca/PVB/Harrison/DoubleSlit/DoubleSlit.html)
Slit 2 open:
Now we measure
the probability P2
of finding a bullet
a distance x from
the center.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A Double Slit Experiment with Bullets
Imagine a Drunkard spraying bullets with a Gun randomly in all
directions.
(All images in this section from: http://www.upscale.utoronto.ca/PVB/Harrison/DoubleSlit/DoubleSlit.html)
both the slits
open:
We measure the
probability
P12 = P1 + P2 of
finding a bullet a
distance x from
the center.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A Double Slit Experiment with Bullets
Imagine a Drunkard spraying bullets with a Gun randomly in all
directions.
(All images in this section from: http://www.upscale.utoronto.ca/PVB/Harrison/DoubleSlit/DoubleSlit.html)
Definition of Particle Nature
A physical entity has a particle nature if its probability
distribution adds in the manner of bullets when it is subjected to
two slit experiment.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Ripple Tank Experiment to Demonstrate Wave Nature
Consider tapping the surface of a water filled tank and just as
before we have two slits.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Ripple Tank Experiment to Demonstrate Wave Nature
Consider tapping the surface of a water filled tank and just as
before we have two slits.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Ripple Tank Experiment to Demonstrate Wave Nature
Consider tapping the surface of a water filled tank and just as
before we have two slits.
Slit 1 open:
We can measure the
Intensity distribution of wave
energy arriving at the
backstop I1 = |h1 |2 at any
distance x from the center.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Ripple Tank Experiment to Demonstrate Wave Nature
Consider tapping the surface of a water filled tank and just as
before we have two slits.
Slit 2 open:
Now we measure the
intensity I2 = |h|2 at any
distance x from the center.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Ripple Tank Experiment to Demonstrate Wave Nature
Consider tapping the surface of a water filled tank and just as
before we have two slits.
Both the slits open:
We measure the intensity
I12 = |h1 + h2 |2
I12 = |h1 |2 + |h2 |2
+2|h1 ||h2 |cosδ
at a distance x from the
center.Notice the
interference pattern – it is the
signature of wave nature
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Ripple Tank Experiment to Demonstrate Wave Nature
Consider tapping the surface of a water filled tank and just as
before we have two slits.
Constructive Interference
Waves are in phase
Destructive Interference
Waves are out of phase
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Ripple Tank Experiment to Demonstrate Wave Nature
Consider tapping the surface of a water filled tank and just as
before we have two slits.
Definition of wave nature
A physical entity has a wave nature if its intensity distribution
shows interference pattern when it is subjected to two slit
experiment.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Cracking the Identity of Electrons:
Two Slit Experiment with Electrons
Consider a “thought” experiment with electrons fired from an
electron gun and passing through two slits as before
Every TV houses an Electron Gun
“Everybody knows” electrons are particles. They after all have
mass ∼ 10−30 Kg. Lets crack the identity once and for all.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Probing the shady behavior of electrons
Flash animation (shown separately) from David Harrison
(university of Toronto) to demonstrate that interference pattern
is produced even if we allow only one electron at a time.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Probing the shady behavior of electrons
Interpretation 1: May be the electrons passing through
the two slits are conspiring to produce the interference
pattern.
This does not seem to be the case as even when you allow
one electron at a time, after waiting for sufficiently long
time, they still produce the interference pattern
Employ Detectives: Track their path and observe their
shady behavior.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Probing the shady behavior of electrons
No interference pattern produced. This is very very strange and
weird !
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Double-slit: Not just a thought experiment
Tonomura at Hitachi labs actually observed
interference
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Heisenberg’s Uncertainty:
Position and Momentum are at Loggerhead
In order to pin down which hole the electron went through,
we need to measure its position fairly accurately.
To resolve the position accurately, we need to use a probe
(light) of very small wavelength, i.e., high frequency and
hence high energy. This would impart large momentum to
the electron and make its momentum very uncertain.
To measure momentum fairly accurately we need to use
light of low frequency and hence low energy. Unfortunately
such a probe will have large wavelength and hence
position cannot be resolved accurately.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
Light on light
Transverse EM waves.
EM fields oscillate in XY plane if wave is travelling along
~ is
z-axis. Light is plane (linearly) polarized when E
~ = Ex î + Ey ĵ.
oscillating in a fixed direction. E
Wave nature of light cannot explain photoelectric effect.
Ejection of electrons from the metal surace when we shine
x-rays, can be explained only when we assume that light
consists of a stream of particles called photons.
When plane polarized light is incident on a metal electrons
are ejected in a preferred direction. Thus polarization
properties are clearly connected with particle properties of
light and we must be a state of polarization to photons.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
Light on light
Transverse EM waves.
EM fields oscillate in XY plane if wave is travelling along
~ is
z-axis. Light is plane (linearly) polarized when E
~ = Ex î + Ey ĵ.
oscillating in a fixed direction. E
Wave nature of light cannot explain photoelectric effect.
Ejection of electrons from the metal surace when we shine
x-rays, can be explained only when we assume that light
consists of a stream of particles called photons.
When plane polarized light is incident on a metal electrons
are ejected in a preferred direction. Thus polarization
properties are clearly connected with particle properties of
light and we must be a state of polarization to photons.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
Light on light
Transverse EM waves.
EM fields oscillate in XY plane if wave is travelling along
~ is
z-axis. Light is plane (linearly) polarized when E
~ = Ex î + Ey ĵ.
oscillating in a fixed direction. E
Wave nature of light cannot explain photoelectric effect.
Ejection of electrons from the metal surace when we shine
x-rays, can be explained only when we assume that light
consists of a stream of particles called photons.
When plane polarized light is incident on a metal electrons
are ejected in a preferred direction. Thus polarization
properties are clearly connected with particle properties of
light and we must be a state of polarization to photons.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
Light on light
Transverse EM waves.
EM fields oscillate in XY plane if wave is travelling along
~ is
z-axis. Light is plane (linearly) polarized when E
~ = Ex î + Ey ĵ.
oscillating in a fixed direction. E
Wave nature of light cannot explain photoelectric effect.
Ejection of electrons from the metal surace when we shine
x-rays, can be explained only when we assume that light
consists of a stream of particles called photons.
When plane polarized light is incident on a metal electrons
are ejected in a preferred direction. Thus polarization
properties are clearly connected with particle properties of
light and we must be a state of polarization to photons.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
Polaroid Filters: Sorting unpolarized light
Light from sun is unpolarized
A polaroid filter (such as tourmaline crystal) allows light of
only certain fixed polarization (one that is normal to its
optic axis)
Let us obtain a polarized beam by passing unpolarized
light through polaroid filter.
If we now let this light beam incident on another tourmaline
crystal such that its polarization makes at an angle α to the
optic axis of crystal then a fraction sin2 α will go through.
So far so good.
When you think of this in terms of photon picture you are in
deep trouble!
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
Polaroid Filters: Sorting unpolarized light
Light from sun is unpolarized
A polaroid filter (such as tourmaline crystal) allows light of
only certain fixed polarization (one that is normal to its
optic axis)
Let us obtain a polarized beam by passing unpolarized
light through polaroid filter.
If we now let this light beam incident on another tourmaline
crystal such that its polarization makes at an angle α to the
optic axis of crystal then a fraction sin2 α will go through.
So far so good.
When you think of this in terms of photon picture you are in
deep trouble!
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
Polaroid Filters: Sorting unpolarized light
Light from sun is unpolarized
A polaroid filter (such as tourmaline crystal) allows light of
only certain fixed polarization (one that is normal to its
optic axis)
Let us obtain a polarized beam by passing unpolarized
light through polaroid filter.
If we now let this light beam incident on another tourmaline
crystal such that its polarization makes at an angle α to the
optic axis of crystal then a fraction sin2 α will go through.
So far so good.
When you think of this in terms of photon picture you are in
deep trouble!
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
Polaroid Filters: Sorting unpolarized light
Light from sun is unpolarized
A polaroid filter (such as tourmaline crystal) allows light of
only certain fixed polarization (one that is normal to its
optic axis)
Let us obtain a polarized beam by passing unpolarized
light through polaroid filter.
If we now let this light beam incident on another tourmaline
crystal such that its polarization makes at an angle α to the
optic axis of crystal then a fraction sin2 α will go through.
So far so good.
When you think of this in terms of photon picture you are in
deep trouble!
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
Polaroid Filters: Sorting unpolarized light
Light from sun is unpolarized
A polaroid filter (such as tourmaline crystal) allows light of
only certain fixed polarization (one that is normal to its
optic axis)
Let us obtain a polarized beam by passing unpolarized
light through polaroid filter.
If we now let this light beam incident on another tourmaline
crystal such that its polarization makes at an angle α to the
optic axis of crystal then a fraction sin2 α will go through.
So far so good.
When you think of this in terms of photon picture you are in
deep trouble!
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
Being photon!
A plane polarized photon when confronted with tourmaline
crystal it is thorroughly confused
to pass through unscathed
totally submit and get absorbed
dvide into half and let the half of him pass by and the other
half be absorbed
Just toss a coin and decide
Someone please shed light on light!
A photon who sheds light on everything else finds himself
totally in dark.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
Being photon!
A plane polarized photon when confronted with tourmaline
crystal it is thorroughly confused
to pass through unscathed
totally submit and get absorbed
dvide into half and let the half of him pass by and the other
half be absorbed
Just toss a coin and decide
Someone please shed light on light!
A photon who sheds light on everything else finds himself
totally in dark.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
Outline
1
prelude
2
Course Structure
3
Quantum Shock
4
Being Photon
A twist in the spin
5
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
Breaking News!–
Indiscrete spinning (h)-barred!
Charged electron orbiting the nucleus forms a current loop
i.e., a tiny magnetic dipole µ
Electrons also possess spin and hence µs
Ain’t it electron’s discretion how fast to spin and where to
orient itself.If a certain Mr. B (magnetic field) pops up,
shouldn’t electron decide how cozy (what angle) it can get
with him?
Alas, electron can only be a friend (parallel) or a
foe(anti-parallel). Proof: When in the magnetic field B, the
µs · B interaction splits the atomic energy levels.
Experiment by Stern and Gerlach (1921) directly
demonstrated this beyond any doubt.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
Breaking News!–
Indiscrete spinning (h)-barred!
Charged electron orbiting the nucleus forms a current loop
i.e., a tiny magnetic dipole µ
Electrons also possess spin and hence µs
Ain’t it electron’s discretion how fast to spin and where to
orient itself.If a certain Mr. B (magnetic field) pops up,
shouldn’t electron decide how cozy (what angle) it can get
with him?
Alas, electron can only be a friend (parallel) or a
foe(anti-parallel). Proof: When in the magnetic field B, the
µs · B interaction splits the atomic energy levels.
Experiment by Stern and Gerlach (1921) directly
demonstrated this beyond any doubt.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
Breaking News!–
Indiscrete spinning (h)-barred!
Charged electron orbiting the nucleus forms a current loop
i.e., a tiny magnetic dipole µ
Electrons also possess spin and hence µs
Ain’t it electron’s discretion how fast to spin and where to
orient itself.If a certain Mr. B (magnetic field) pops up,
shouldn’t electron decide how cozy (what angle) it can get
with him?
Alas, electron can only be a friend (parallel) or a
foe(anti-parallel). Proof: When in the magnetic field B, the
µs · B interaction splits the atomic energy levels.
Experiment by Stern and Gerlach (1921) directly
demonstrated this beyond any doubt.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
Breaking News!–
Indiscrete spinning (h)-barred!
Charged electron orbiting the nucleus forms a current loop
i.e., a tiny magnetic dipole µ
Electrons also possess spin and hence µs
Ain’t it electron’s discretion how fast to spin and where to
orient itself.If a certain Mr. B (magnetic field) pops up,
shouldn’t electron decide how cozy (what angle) it can get
with him?
Alas, electron can only be a friend (parallel) or a
foe(anti-parallel). Proof: When in the magnetic field B, the
µs · B interaction splits the atomic energy levels.
Experiment by Stern and Gerlach (1921) directly
demonstrated this beyond any doubt.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
Breaking News!–
Indiscrete spinning (h)-barred!
Charged electron orbiting the nucleus forms a current loop
i.e., a tiny magnetic dipole µ
Electrons also possess spin and hence µs
Ain’t it electron’s discretion how fast to spin and where to
orient itself.If a certain Mr. B (magnetic field) pops up,
shouldn’t electron decide how cozy (what angle) it can get
with him?
Alas, electron can only be a friend (parallel) or a
foe(anti-parallel). Proof: When in the magnetic field B, the
µs · B interaction splits the atomic energy levels.
Experiment by Stern and Gerlach (1921) directly
demonstrated this beyond any doubt.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
The Classic Stern-Gerlach Experiment
They sent a collimated beam of Ag atoms through the
inhomogeneous magnetic field.
Riding on each of the Ag atom was an unpaired (47th ) electron
whose spin provides the angular momentum s and hence a
magnetic moment µ = −es
mc .
Interaction energy: −µ · B
∂
z
Force in the inhomogeneous B: Fz = − ∂z
(µ · B) = −µz ∂B
∂z
Ag atoms experience upward or downward force depending
upon their spin orientation.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
The Classic Stern-Gerlach Experiment
They sent a collimated beam of Ag atoms through the
inhomogeneous magnetic field.
Riding on each of the Ag atom was an unpaired (47th ) electron
whose spin provides the angular momentum s and hence a
magnetic moment µ = −es
mc .
Interaction energy: −µ · B
∂
z
Force in the inhomogeneous B: Fz = − ∂z
(µ · B) = −µz ∂B
∂z
Ag atoms experience upward or downward force depending
upon their spin orientation.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
The Classic Stern-Gerlach Experiment
They sent a collimated beam of Ag atoms through the
inhomogeneous magnetic field.
Riding on each of the Ag atom was an unpaired (47th ) electron
whose spin provides the angular momentum s and hence a
magnetic moment µ = −es
mc .
Interaction energy: −µ · B
∂
z
Force in the inhomogeneous B: Fz = − ∂z
(µ · B) = −µz ∂B
∂z
Ag atoms experience upward or downward force depending
upon their spin orientation.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
The Classic Stern-Gerlach Experiment
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
The Classic Stern-Gerlach Experiment
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
The Classic Stern-Gerlach Experiment
Angular Momentum orientation is quantized !
For s = 1/2 particles, only two (2s + 1) projections about z-axis
are allowed and not a continuum of values possibles.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
Sequential Stern-Gerlach Experiment
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
Sequential Stern-Gerlach Experiment
No big deal!
You have blocked Sz− , so obviously you won’t find them in the
second SG apparatus. It is elementary sir!
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
Sequential Stern-Gerlach Experiment
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
Sequential Stern-Gerlach Experiment
This is weird!
From where on earth did you pull out the Sx+ and the Sx−
components. Well, may be the 50% of Sz+ atoms from the first
SG apparatus are Sz+ and Sx+ and the remaining 50% are Sz+
and Sx− . Sounds weird but looks like the only explanation. Not
elementary anymore though!
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
Sequential Stern-Gerlach Experiment
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
Sequential Stern-Gerlach Experiment
Phew!
Wasn’t the Sz− component gobbled up by the first apparatus
already? Is this Physics or paraphysics? Neither elementary
nor satisfactory!
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
Sequential Stern-Gerlach Experiment
Welcome to QMech-1
Nature unfortunately never confirmed to our intuition before she
wrote her most beautiful songs. You just had your first brush
with the non-commuting observables. In QM you cannot
determine Sx and Sz simultaneously. Measuring one will
destroy the other completely and beyond any memory.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
A Quantum Paradigm Shift: Peeping Through the
Quantum Veil
The Quantum Wonderland lies beyond the boundaries
of classical objective reality, certainty, and
determinism. It seems like nature is hiding her reality
in a “mysterious and mind reading quantum veil” that
seems to know when you are watching and what you
are wanting ! The quantum world sure redefines the
“classical” task of Physics. Neils Bohr has famously
said, “The business of Physics is not to describe how
nature is but what we can say about nature.”
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
Coming to Terms with the Quantum Shock:
Reality Check!
What is reality after all? Isn’t our notion of reality built
from classical perceptions? Are we justified in our
unqualified extrapolations down to the bottom-most
layer of nature? Isn’t the classical world “sensible”
because the Quantum world is “Weired”? Just to put
our weired expectation and extrapolations in place –
given the details of marks of every student we can
sure construct the average; but given the “average” we
can never construct the distribution. From this
perspective, the quantum shock was as much our
absurd expectation of unqualified extrapolation as
much it was nature’s mystery.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
The agony irony and the ecstasy of being an electron
I am here I am there
When I am free
I am everywhere
Try and find me (You peeping Toms)
And I collapse anywhere.
When I am bang on
Am momentously uncertain
But with a focused momentum
Am all over for certain.
Try and cage me
And I hit hard on the walls
The smaller your cage
Harder I hit.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
The agony irony and the ecstasy of being an electron
Inside of a tiny prison h-bar
Am never bored and lonesome
As flabbergast you watch
An army of electrons
Merrily dancing and giggling
Arms around the waist
With the hottest of positrons.
Bewildered and stung in disbelief you ask
What on earth is happening
It sure takes two to tango
Oh! but you can’t have too much fun
Flirting with a lonesome electron
Squeezing it to size h-bar
With c-through walls.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
The agony irony and the ecstasy of being an electron
As you wonder and deliberate
If I am a reality-check on your fantasy
Or a disillusioned physicist’s fantasy
I embrace all uncertainties
With best of my potential
At best a probability
Doomed in anonymity
Am a waving particle
Perhaps a particulate wave
Neither Gods of any religion
Nor their best children
Could settle on my coordinates
Or give me a decent name.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
A twist in the spin
The agony irony and the ecstasy of being an electron
It is my agony and an irony
Am the stuff that stuffs all the stuff
But God only knows the stuff I am
Or may be
She is clueless too!
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
Outline
1
prelude
2
Course Structure
3
Quantum Shock
4
Being Photon
A twist in the spin
5
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
An advice that may have “aborted” Quantum Physics
before conception!
Young man, replied Jolly. Why do you want to ruin
your life? The theoretical physics is practically
finished, the differential equations have all been
solved. All that is left now is to consider individual
special cases involving variations of initial boundary
conditions. Is it worthwhile taking up a job which does
not hold prospects for the future?
Philip Jolly, Max Planck’s teacher and mentor, on
being consulted by Max Planck about career in
Physics
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
An advice that may have “aborted” Quantum Physics
before conception!
Young man, replied Jolly. Why do you want to ruin
your life? The theoretical physics is practically
finished, the differential equations have all been
solved. All that is left now is to consider individual
special cases involving variations of initial boundary
conditions. Is it worthwhile taking up a job which does
not hold prospects for the future?
Philip Jolly, Max Planck’s teacher and mentor, on
being consulted by Max Planck about career in
Physics
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
A Hike to the Summit
Instead of the customary helicopter areal survey, we shall take
a slightly more detailed climb to the summit of Planck’s formula
for the following reasons:
All your future courses shall only do a lip service, since it
truly falls in the domain of “modern physics“.
It is not sufficiently modern for typical 21st century modern
physics courses and hence hurriedly gobbled up.
To me however it truly demonstrates unity and synthesis of
various branches of physics like mechanics,
electrodynamics, thermodynamics and statistical physics.
Nature knows no compartments. What is more it is a
brilliant example of how the whole sometimes is just not
the sum of the parts – an uneasy calm before the storm.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
A Hike to the Summit
Instead of the customary helicopter areal survey, we shall take
a slightly more detailed climb to the summit of Planck’s formula
for the following reasons:
All your future courses shall only do a lip service, since it
truly falls in the domain of “modern physics“.
It is not sufficiently modern for typical 21st century modern
physics courses and hence hurriedly gobbled up.
To me however it truly demonstrates unity and synthesis of
various branches of physics like mechanics,
electrodynamics, thermodynamics and statistical physics.
Nature knows no compartments. What is more it is a
brilliant example of how the whole sometimes is just not
the sum of the parts – an uneasy calm before the storm.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
A Hike to the Summit
Instead of the customary helicopter areal survey, we shall take
a slightly more detailed climb to the summit of Planck’s formula
for the following reasons:
All your future courses shall only do a lip service, since it
truly falls in the domain of “modern physics“.
It is not sufficiently modern for typical 21st century modern
physics courses and hence hurriedly gobbled up.
To me however it truly demonstrates unity and synthesis of
various branches of physics like mechanics,
electrodynamics, thermodynamics and statistical physics.
Nature knows no compartments. What is more it is a
brilliant example of how the whole sometimes is just not
the sum of the parts – an uneasy calm before the storm.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
A Hike to the Summit
Instead of the customary helicopter areal survey, we shall take
a slightly more detailed climb to the summit of Planck’s formula
for the following reasons:
All your future courses shall only do a lip service, since it
truly falls in the domain of “modern physics“.
It is not sufficiently modern for typical 21st century modern
physics courses and hence hurriedly gobbled up.
To me however it truly demonstrates unity and synthesis of
various branches of physics like mechanics,
electrodynamics, thermodynamics and statistical physics.
Nature knows no compartments. What is more it is a
brilliant example of how the whole sometimes is just not
the sum of the parts – an uneasy calm before the storm.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
The Problem of Blackbody Radiation (BBR)
Blackbody: An idealized physical body that absorbs (and
does not reflect) all the incident radiation regardless of the
frequency and the angle. In thermal equilibrium it also emits
light in all frequency and in all directions (isotropic).
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
The Problem of Blackbody Radiation (BBR)
Blackbody: An idealized physical body that absorbs (and
does not reflect) all the incident radiation regardless of the
frequency and the angle. In thermal equilibrium it also emits
light in all frequency and in all directions (isotropic).
The Problem
Theoretically explain how the
energy density of the radiation is
distributed in different frequencies
at different temperature.
We will first try and understand a
different problem to appreciate this
problem and its resolution.
image source:hephaestusaudio.com
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
A Different Problem: Apportioning of Total Energy
Imagine an object immersed in a thermal reservoir is in a state
of thermal equilibrium.
Though there is no apparent thermal exchange between the
object and the reservoir, the actual energy of the molecules of
the object fluctuate around some average value.
Using Boltzman’s statistical mechanics, we can say something
about this fluctuations, i.e., what is the distribution of molecular
speeds.That is, how is the total energy of the object partitioned
amongst its constituent molecules and atoms
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
A Different Problem: Apportioning of Total Energy
Imagine an object immersed in a thermal reservoir is in a state
of thermal equilibrium.
Though there is no apparent thermal exchange between the
object and the reservoir, the actual energy of the molecules of
the object fluctuate around some average value.
Using Boltzman’s statistical mechanics, we can say something
about this fluctuations, i.e., what is the distribution of molecular
speeds.That is, how is the total energy of the object partitioned
amongst its constituent molecules and atoms
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
A Different Problem: Apportioning of Total Energy
Imagine an object immersed in a thermal reservoir is in a state
of thermal equilibrium.
Though there is no apparent thermal exchange between the
object and the reservoir, the actual energy of the molecules of
the object fluctuate around some average value.
Using Boltzman’s statistical mechanics, we can say something
about this fluctuations, i.e., what is the distribution of molecular
speeds.That is, how is the total energy of the object partitioned
amongst its constituent molecules and atoms
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
More Precisely
The state of a dynamical system with f DOF is specified by
giving the coordinates q1 , q2 , ...qf and corresponding momenta
p1 , p2 , ...pf . All these, as well as the energy
E(q1 , q2 , ...qf , p1 , p2 , ...pf ) of the system varies with time (since
it is exchanging energy with the reservoir at microscopic level).
What is the probability for q1 , q2 , ... to take values between q1
and q1 + dq1 , q2 and q2 + dq2 , ...and, at the same time for the
p1 , p2 ...to take some values between p1 and p1 + dp1 , p2 and
p2 + dP2 , ... respectively?
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
More Precisely
Boltzman’s answer:
P(q1 q2 ...qf p1 p2 ...pf )dq1 dq2 ...dqf dp1 dp2 ...dpf
1
= A exp −
E(q1 q2 ...qf p1 p2 ...pf )
KT
dq1 dq2 ...dqf dp1 dp2 ...dpf
1
A= RR R
1
... exp − KT E(q1 q2 ...qf p1 p2 ...pf ) dq1 ...dqf dp1 ...dpf
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
An Important Conclusion
As long as KE of each DOF is proportional to square of
momentum, i.e.,:
Ekin = α1 p12 + α2 p22 + ... + αf pf2
Law of Equipartition of Energy
Average value of the kinetic energy per degree of freedom in
the reservoir at temperature T is:
< αs ps2 >=
Rishikesh Vaidya
1
kT
2
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
An Important Conclusion
As long as KE of each DOF is proportional to square of
momentum, i.e.,:
Ekin = α1 p12 + α2 p22 + ... + αf pf2
Law of Equipartition of Energy
Average value of the kinetic energy per degree of freedom in
the reservoir at temperature T is:
< αs ps2 >=
Rishikesh Vaidya
1
kT
2
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
Energy of Unit Mole (N = 6.02 × 1023 ) of a Substance
Ideal Monatomic Gas
U = Ekin = ΣN
n=1
1
2
2
(p2 + pny
+ pnz
)
2m nx
1
3N kT
(3N ∗ Average Value per DOF)
2
3
RT
(R = Nk = 1.98 cal/o K : Gas constant)
2
Specific Heat: The necessary heat C to raise the temperature
by 1o is:
3
C = R = 2.97 cal/o K
2
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
Energy of Unit Mole (N = 6.02 × 1023 ) of a Substance
Ideal Diatomic Gas: 5 degrees of freedom (3 trans. + 2 rot.)
U =
C =
5
RT
2
5
R = 4.95 cal/o K
2
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
Energy of Unit Mole (N = 6.02 × 1023 ) of a Substance
Crystalline Substance
Atoms on lattice perform random small oscillations.
Any arbitrary mode of oscillation consists of superposition
of normal modes of oscillations.
No. of normal modes = No. of DOF.
Energy of the sth normal mode is: Es = αs ps2 + βs qs2 .
Law of Equipartition holds: < αs ps2 >=< βs qs2 >= 21 kT .
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
Energy of Unit Mole (N = 6.02 × 1023 ) of a Substance
Crystalline Substance
So for f normal modes:
< E > = fkT
U = 3NkT = 3RT
f = 3N
o
C = 3R = 5.85 cal/ K
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
Specific Heat “feels the heat”!
source: Quantum Mechanics by Tomonaga
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
Specific Heat “feels the heat”!
Molar specific heat for hydrogen.
source: Quantum Mechanics by Tomonaga
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
Specific Heat “feels the heat”!
Molar specific heat for lead(Pb).
source: Quantum Mechanics by Tomonaga
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
Specific Heat “feels the heat”!
Cracks Appear: Fall of the Law of Equipartition !
The figures amply show that agreement is great at
comparatively high temperature but theory fails badly at low
temperatures. This could mean that at low temperatures not
every degree of freedom receives enough energy to satisfy the
law of equipartition of energy.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
What does it cost to heat “Vacuum”!
At low temperatures energy is not equitably shared
amongst all the DOF of a system.
This is even more striking in case of “vacuum”!
Let us immerse “vacuum” in our reservoir; that is a hollow
cavity surrounded by walls of temperature T .
Despite being hollow, the cavity contains random
oscillations of electromagnetic fields and hence it has
some thermal energy. We can then consider specific heat
of “vacuum” itself.
Any arbitrary mode of oscillation can be written as a
superposition of normal modes. Thus the EM fields inside
the cavity can be considered to be a collection
independent harmonic oscillators.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
What does it cost to heat “Vacuum”!
At low temperatures energy is not equitably shared
amongst all the DOF of a system.
This is even more striking in case of “vacuum”!
Let us immerse “vacuum” in our reservoir; that is a hollow
cavity surrounded by walls of temperature T .
Despite being hollow, the cavity contains random
oscillations of electromagnetic fields and hence it has
some thermal energy. We can then consider specific heat
of “vacuum” itself.
Any arbitrary mode of oscillation can be written as a
superposition of normal modes. Thus the EM fields inside
the cavity can be considered to be a collection
independent harmonic oscillators.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
What does it cost to heat “Vacuum”!
At low temperatures energy is not equitably shared
amongst all the DOF of a system.
This is even more striking in case of “vacuum”!
Let us immerse “vacuum” in our reservoir; that is a hollow
cavity surrounded by walls of temperature T .
Despite being hollow, the cavity contains random
oscillations of electromagnetic fields and hence it has
some thermal energy. We can then consider specific heat
of “vacuum” itself.
Any arbitrary mode of oscillation can be written as a
superposition of normal modes. Thus the EM fields inside
the cavity can be considered to be a collection
independent harmonic oscillators.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
What does it cost to heat “Vacuum”!
At low temperatures energy is not equitably shared
amongst all the DOF of a system.
This is even more striking in case of “vacuum”!
Let us immerse “vacuum” in our reservoir; that is a hollow
cavity surrounded by walls of temperature T .
Despite being hollow, the cavity contains random
oscillations of electromagnetic fields and hence it has
some thermal energy. We can then consider specific heat
of “vacuum” itself.
Any arbitrary mode of oscillation can be written as a
superposition of normal modes. Thus the EM fields inside
the cavity can be considered to be a collection
independent harmonic oscillators.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
What does it cost to heat “Vacuum”!
At low temperatures energy is not equitably shared
amongst all the DOF of a system.
This is even more striking in case of “vacuum”!
Let us immerse “vacuum” in our reservoir; that is a hollow
cavity surrounded by walls of temperature T .
Despite being hollow, the cavity contains random
oscillations of electromagnetic fields and hence it has
some thermal energy. We can then consider specific heat
of “vacuum” itself.
Any arbitrary mode of oscillation can be written as a
superposition of normal modes. Thus the EM fields inside
the cavity can be considered to be a collection
independent harmonic oscillators.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
Whatever happened to Stefan’s law (U = σT 4 )!
Mathematically, we can describe the state of EM field in terms
of normal coordinates q1 , q2 , q3 , .. and corresponding
p1 , p2 , p3 , .... The energy of a state is given as a sum of terms
Es = αs ps2 + βs qs2 .
We can then apportion the total energy amongst each of these
f DOF using Law of equipartition. Thus E = fkT .
But how many DOF (normal modes) does a (continuum)
system of EM fields has? Infinite! A cavity contains infinitely
many normal modes up to arbitrary small wavelengths.
Since f = ∞, E = ∞ and hence Specific heat of “vacuum” is ∞
too! Hollow cavity will endlessly “drink heat” from the reservoir,
Rishikesh Vaidya
QM-1
feeding into normal modes
of shorter
and shorter wavelengths.
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
Whatever happened to Stefan’s law (U = σT 4 )!
Mathematically, we can describe the state of EM field in terms
of normal coordinates q1 , q2 , q3 , .. and corresponding
p1 , p2 , p3 , .... The energy of a state is given as a sum of terms
Es = αs ps2 + βs qs2 .
We can then apportion the total energy amongst each of these
f DOF using Law of equipartition. Thus E = fkT .
But how many DOF (normal modes) does a (continuum)
system of EM fields has? Infinite! A cavity contains infinitely
many normal modes up to arbitrary small wavelengths.
Since f = ∞, E = ∞ and hence Specific heat of “vacuum” is ∞
too! Hollow cavity will endlessly “drink heat” from the reservoir,
Rishikesh Vaidya
QM-1
feeding into normal modes
of shorter
and shorter wavelengths.
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
Whatever happened to Stefan’s law (U = σT 4 )!
Mathematically, we can describe the state of EM field in terms
of normal coordinates q1 , q2 , q3 , .. and corresponding
p1 , p2 , p3 , .... The energy of a state is given as a sum of terms
Es = αs ps2 + βs qs2 .
We can then apportion the total energy amongst each of these
f DOF using Law of equipartition. Thus E = fkT .
But how many DOF (normal modes) does a (continuum)
system of EM fields has? Infinite! A cavity contains infinitely
many normal modes up to arbitrary small wavelengths.
Since f = ∞, E = ∞ and hence Specific heat of “vacuum” is ∞
too! Hollow cavity will endlessly “drink heat” from the reservoir,
Rishikesh Vaidya
QM-1
feeding into normal modes
of shorter
and shorter wavelengths.
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
Whatever happened to Stefan’s law (U = σT 4 )!
Mathematically, we can describe the state of EM field in terms
of normal coordinates q1 , q2 , q3 , .. and corresponding
p1 , p2 , p3 , .... The energy of a state is given as a sum of terms
Es = αs ps2 + βs qs2 .
We can then apportion the total energy amongst each of these
f DOF using Law of equipartition. Thus E = fkT .
But how many DOF (normal modes) does a (continuum)
system of EM fields has? Infinite! A cavity contains infinitely
many normal modes up to arbitrary small wavelengths.
Since f = ∞, E = ∞ and hence Specific heat of “vacuum” is ∞
too! Hollow cavity will endlessly “drink heat” from the reservoir,
Rishikesh Vaidya
QM-1
feeding into normal modes
of shorter
and shorter wavelengths.
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
Whatever happened to Stefan’s law (U = σT 4 )!
Mathematically, we can describe the state of EM field in terms
of normal coordinates q1 , q2 , q3 , .. and corresponding
p1 , p2 , p3 , .... The energy of a state is given as a sum of terms
Es = αs ps2 + βs qs2 .
We can then apportion the total energy amongst each of these
f DOF using Law of equipartition. Thus E = fkT .
But how many DOF (normal modes) does a (continuum)
system of EM fields has? Infinite! A cavity contains infinitely
many normal modes up to arbitrary small wavelengths.
Since f = ∞, E = ∞ and hence Specific heat of “vacuum” is ∞
too! Hollow cavity will endlessly “drink heat” from the reservoir,
Rishikesh Vaidya
QM-1
feeding into normal modes
of shorter
and shorter wavelengths.
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
Whatever happened to Stefan’s law (U = σT 4 )!
Mathematically, we can describe the state of EM field in terms
of normal coordinates q1 , q2 , q3 , .. and corresponding
p1 , p2 , p3 , .... The energy of a state is given as a sum of terms
Es = αs ps2 + βs qs2 .
We can then apportion the total energy amongst each of these
f DOF using Law of equipartition. Thus E = fkT .
But how many DOF (normal modes) does a (continuum)
system of EM fields has? Infinite! A cavity contains infinitely
many normal modes up to arbitrary small wavelengths.
Since f = ∞, E = ∞ and hence Specific heat of “vacuum” is ∞
too! Hollow cavity will endlessly “drink heat” from the reservoir,
Rishikesh Vaidya
QM-1
feeding into normal modes
of shorter
and shorter wavelengths.
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
Counting the “Caged” Normal Modes
Figure source: Quantum Mechanics by Tomonaga (vol.1)
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
Counting the “Caged” Normal Modes
Assignment 1(a): Consider a string of length L fixed at two
ends. If the velocity of elastic waves on this string is c, show
that the number of normal modes contained in frequency range
between ν and ν + dν is
Z (ν)dν =
Rishikesh Vaidya
2L
dν
c
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
Counting the “Caged” Normal Modes
Assignment 1(b):Following the same method as above, 3-D
oscillations in a cube of side L can be specified by sets of three
positive integers, sx , sy , s and sz . Show that for the case of EM
waves number of oscillations with frequencies between ν and
ν + dν is give by:
Z (ν)dν =
Rishikesh Vaidya
8πL3 2
ν dν
c3
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
A “hole” in the argument!
Boundary conditions: We assumed the ends of strings rigidly
tied at the ends. This implies that string exchanges no energy
with the surroundings. Analogously we must assume perfectly
reflecting mirrors of the cavity wherein our EM fields are caged.
How do we achieve thermal equilibrium then?
We drill a small hole in the cavity that is big enough to allow
thermal equilibrium via exchange with reservoir but small
enough to not disturb our calculation of number of normal
modes.
Following equipartition we obtain total energy
E(ν)dν = Z (ν)dν × kT
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
A “hole” in the argument!
Boundary conditions: We assumed the ends of strings rigidly
tied at the ends. This implies that string exchanges no energy
with the surroundings. Analogously we must assume perfectly
reflecting mirrors of the cavity wherein our EM fields are caged.
How do we achieve thermal equilibrium then?
We drill a small hole in the cavity that is big enough to allow
thermal equilibrium via exchange with reservoir but small
enough to not disturb our calculation of number of normal
modes.
Following equipartition we obtain total energy
E(ν)dν = Z (ν)dν × kT
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
A “hole” in the argument!
Boundary conditions: We assumed the ends of strings rigidly
tied at the ends. This implies that string exchanges no energy
with the surroundings. Analogously we must assume perfectly
reflecting mirrors of the cavity wherein our EM fields are caged.
How do we achieve thermal equilibrium then?
We drill a small hole in the cavity that is big enough to allow
thermal equilibrium via exchange with reservoir but small
enough to not disturb our calculation of number of normal
modes.
Following equipartition we obtain total energy
E(ν)dν = Z (ν)dν × kT
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
A “hole” in the argument!
Boundary conditions: We assumed the ends of strings rigidly
tied at the ends. This implies that string exchanges no energy
with the surroundings. Analogously we must assume perfectly
reflecting mirrors of the cavity wherein our EM fields are caged.
How do we achieve thermal equilibrium then?
We drill a small hole in the cavity that is big enough to allow
thermal equilibrium via exchange with reservoir but small
enough to not disturb our calculation of number of normal
modes.
Following equipartition we obtain total energy
E(ν)dν = Z (ν)dν × kT
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
The First Base Camp
Rayleigh-Jeans Formula
E(ν)dν = Z (ν)dν × kT
8πL3 2
=
ν dνkT
c3
8πkT 2
U(ν)dν =
ν dν
c3
Although we have considered EM waves caged in cube of side
L, it is applicable more generally, without regard to the nature
and shape of walls. Integration over ν diverges as expected
from the law of equipartition of energy. However, for small
frequency Rayleigh-Jeans (RJ) formula does accurately
describe the black body
curve. QM-1
Rishikesh Vaidya
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
Reflections for the Climb Ahead
The agreement of RJ formula extends to higher
frequencies for higher temperatures.
According RJ formula the spectral distribution of light is
independent of temperature but the total intensity is
proportional to it. This implies that color of the light from
the cavity does not depend on the temperature. This is
contrary to experience.
Although energy equipartition does not hold in general but
it still accounts for apportioning of energy to the low
frequencies oscillations, widening its application with
increasing temperature.
This could mean that with decreasing temperature,
degrees of freedom corresponding to large frequencies
start violating the equipartition law and “die”; i.e., energy is
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
Reflections for the Climb Ahead
The agreement of RJ formula extends to higher
frequencies for higher temperatures.
According RJ formula the spectral distribution of light is
independent of temperature but the total intensity is
proportional to it. This implies that color of the light from
the cavity does not depend on the temperature. This is
contrary to experience.
Although energy equipartition does not hold in general but
it still accounts for apportioning of energy to the low
frequencies oscillations, widening its application with
increasing temperature.
This could mean that with decreasing temperature,
degrees of freedom corresponding to large frequencies
start violating the equipartition law and “die”; i.e., energy is
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
Reflections for the Climb Ahead
The agreement of RJ formula extends to higher
frequencies for higher temperatures.
According RJ formula the spectral distribution of light is
independent of temperature but the total intensity is
proportional to it. This implies that color of the light from
the cavity does not depend on the temperature. This is
contrary to experience.
Although energy equipartition does not hold in general but
it still accounts for apportioning of energy to the low
frequencies oscillations, widening its application with
increasing temperature.
This could mean that with decreasing temperature,
degrees of freedom corresponding to large frequencies
start violating the equipartition law and “die”; i.e., energy is
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
Reflections for the Climb Ahead
The agreement of RJ formula extends to higher
frequencies for higher temperatures.
According RJ formula the spectral distribution of light is
independent of temperature but the total intensity is
proportional to it. This implies that color of the light from
the cavity does not depend on the temperature. This is
contrary to experience.
Although energy equipartition does not hold in general but
it still accounts for apportioning of energy to the low
frequencies oscillations, widening its application with
increasing temperature.
This could mean that with decreasing temperature,
degrees of freedom corresponding to large frequencies
start violating the equipartition law and “die”; i.e., energy is
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
Outline
1
prelude
2
Course Structure
3
Quantum Shock
4
Being Photon
A twist in the spin
5
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
Notion of Adiabatic Invariants
Adiabatic Invariants
Adiabatic Invariants are approximate constants of motion
(Invariants) of a given dynamical system, which are preserved
(constant) during a process of very slow change of system’s
parameters.
Examples:
(a) An oscillating pendulum whose string is gradually shortened
or (b) radiation in a hollow cavity sealed from the reservoir and
whose walls are adiabatically compressed. The frequency ν
and amplitude (and hence energy) of the oscillations will
naturally change, however, the ratio E/ν remains constant
during slow deformation.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
Notion of Adiabatic Invariants
Adiabatic Invariants
Adiabatic Invariants are approximate constants of motion
(Invariants) of a given dynamical system, which are preserved
(constant) during a process of very slow change of system’s
parameters.
Examples:
(a) An oscillating pendulum whose string is gradually shortened
or (b) radiation in a hollow cavity sealed from the reservoir and
whose walls are adiabatically compressed. The frequency ν
and amplitude (and hence energy) of the oscillations will
naturally change, however, the ratio E/ν remains constant
during slow deformation.
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
An Example from MEOW!
Image source: Quantum
Mechanics by Tomonaga
Rishikesh Vaidya
Problem: Consider an oscillating
pendulum as shown in figure.
When the string is being pulled
very slowly (on a time scale much
larger than the period T ), show
that average tension
< T >= mg + 14 mgθ02 . Also show
that E/ν is constant.
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
stop here
Rishikesh Vaidya
QM-1
prelude
Course Structure
Quantum Shock
Being Photon
The Road to Planck’s Black Body Radiation
Specific Heat “feels the heat”
Wein’s Law: Displacement in Despair
Quiz-2
A. (a) A collimated beam of Ag atoms from the owen is passed
through SG-x̂. Draw and label the output from SG-x̂. (b) Each of
the output from the previous experiment is subjected to a SG-ẑ.
Label the output. (c) Any one of the output (your choice) from
part(b) is subjected to a SG-ŷ . Label the output. (d) What can
you conclude from above observations (one sentence).
B. (a) What is the property of a polarized material? (b) A beam of
light is incident at an angle of 45o to the optic axis of a polaroid
material. What fraction of light is transmitted? (c) Output beam
in part (a) is fed into another polaroid material whose optic axis
is at an angle α to the optic axis in part(a). What fraction of light
is seen in the output. (d) What can you say when a single
photon was made to incident in part (a).
Rishikesh Vaidya
QM-1