Quantum Mechanics 101
Waves? or Particles?
Interference of Waves and the
Double Slit Experiment

Waves spreading out from two points, such as
waves passing through two slits, will interfere
l
d
Wave crest
Wave trough
Spot of
constructive
interference
Spot of
destructive
interference
The Double-slit experiment for
particles



Particles do not diffract; they either go through a slit or
they don’t
Particles passing through a slit hit a screen only in a small
area; if they all have the same initial velocity, they will all
hit at the exact same point
Particles passing through two slits will form two maxima
in front of the two slits
What Happens if Electrons Pass
Through Small Openings?
What does that tell you about
electrons?
The Plot Thickens
An experiment called the
“photoelectric effect” also gives
unexpected results!
The Photoelectric Effect,
Pictorially

Light shining on a material may be absorbed by electrons in that
The
energy
of the
material
If ankinetic
electron
absorbs
electron
will be to
equal
to the
enough energy
break
energy absorbed by the
free of its
bonds,
can
electron
minus
theitenergy
leave the
needed
to material
free it, provided
the electron does not lose
any energy in collisions
Wave theory predicts . . .
the energy of emitted electrons should
depend on the intensity of light
 electrons will need to soak up energy from
wave for period of time before being ejected
 the frequency of light won’t affect the
maximum kinetic energy of electrons

The Photoelectric Effect,
Experimentally




As a given color (frequency) of light enters the black box-like
photoelectric head, it falls on a plate of electron-emitting material
inside
Emitted electrons are collected on another plate nearby, producing
an electric potential difference between the two plates (like a
capacitor)
When the capacitor is fully charged and no more electrons can be
added, the potential energy of the capacitor equals the maximum
kinetic energy of the electrons trying to leave the original plate
The potential difference on the capacitor at this point is called the
stopping potential Vs for the electrons, and it is proportional to the
maximum kinetic energy of electrons emitted by the light:
K = eVs = Eabsorbed - F
Work function (energy needed
to remove electron)
Do the Photoelectric
Experiment
Upon what does the energy of emitted
electrons appear to depend?
Experiment sees . . .




the energy of emitted electrons does not depend on
the intensity of light
electrons are ejected immediately
the frequency of light does affect the maximum
kinetic energy of electrons; kinetic energy is
linearly dependent on frequency
intensity of light determines number of emitted
electrons (photocurrent)
Einstein to the Rescue

Einstein suggested that light was emitted or absorbed in
particle-like quanta, called photons, of energy, E = hf
If that energy is larger than
an electron
absorbs
theIfwork
function
of the one
of these
photons,can
it gets
metal,
the electron
leave;
if not,hf
it of
can’t:
the entire
energy.
Kmax = Eabs – F = hf - F
Einstein’s Photoelectric
Theory
eVs = Kmax = hf – F




Kmax  f
Is this consistent with what you saw in the experiment?
Electrons are ejected as soon as a photon strikes the
material.
Is this consistent with what you saw in the experiment?
Einstein’s Photoelectric
Theory
eVs = Kmax = hf – F


If hf < F, no electrons are emitted; cutoff
frequency
What should the slope of a K vs. f plot
yield? Is that what you got?
The Conflict
Wave theory accurately describes interference and
diffraction, along with other behavior of light,
such as dispersion and refraction
The particle theory accurately describes
photoelectric effect, black body radiation, and
other experimental results
 Is light a particle? Or is it a wave?
 Is a platypus a duck? Or is it a beaver?
 Am I my mother? Or am I my father?
The Resolution





Light is not either a particle or a wave
Light exhibits wavelike properties when traveling
Light exhibits particlelike properties when
interacting with matter
deBroglie suggested that traditional “particles”,
like the electron, also exhibit wavelike properties
p=h/l, so large (macroscopic) momentum means
small (undetectable) wavelength
The interpretation




Light and “particles” propagate through space as
probability waves
I cannot say for certain where a particle is, where
it was, or how it got to wherever it might have
been
I can, however, say where it is most likely to be
found, where it most likely was, and how likely it
is that it took a particular path
This behavior is described by a wave function
Y(x,y) which obeys Schrödinger’s equation
More interpretation



The probability of finding a particle in a particular
region within a particular time interval is found by
integrating the square of the wave function:
 P (x,t) =  |Y(x,t)|2 dx =  |c(x)|2 dx
|c(x)|2 dx is called the “probability density; the
area under a curve of probability density yields the
probability the particle is in that region
When a measurement is made, we say the wave
function “collapses” to a point, and a particle is
detected at some particular location
What have we learned today?




Quantum mechanics is AWESOME, but it
challenges our physical intuition
Light and “particles” behave like waves when
traveling and like particles when interacting or
being observed
Since they propagate like waves, both light and
“particles” can produce interference patterns
We can describe this duality through the use of a
wave function Y(x,t) which describes the
(unobserved) propagation through space and time