# Notes on Quantum Theory

```QUANTUM MECHANICS (see Chapter 14)
As with nuclear physics (fission and fusion) you've asked
very few questions regarding this area.
In the broadest sense, quantum mechanics attempts to
describe physical behaviour on a very small scale (atomic
or subatomic). So, you wouldn't need quantum mechanics
to describe the motion of a falling rock, but you can use it
to explain how “current” (i.e. moving electrons) can be
created within a “semiconductor” (a material which
doesn't normally carry current, but can do so under
certain conditions).
Of course, everything could be studied on an atomic or
subatomic scale (even if it doesn't have to be), which
means that quantum mechanics is an underlying aspect of
everything!
Quantum physics can be theoretically complex (and can
require very advanced mathematical techniques), so we
won't get into too much depth here. There are some very
simple underlying ideas which can easily be presented,
however.
The Dual Wave/Particle Nature of Light
You have recently heard about the often nasty historical
debate (led by Huygen and Newton and their followers) on
whether light is an electromagnetic wave or a particle
(photon). Long after this issue appeared to have been
settled in favour of the wave side, it turns out that light
actually has a “dual nature”. That is, light exhibits
characteristics of both waves and particles!
Describing the emission of light by an excited atom, in
which an electron first jumps to a higher energy level and
then jumps back down with the ejection of a photon (a
light “particle”) is obviously a quantum mechanical
explanation.
It turns out that the energy E (in Joules) associated with a
particular photon is given by the equation E = hf, where
h = 6.63  10-34 J-s is Planck's constant and f is the “wave
frequency” associated with the photon. (This frequency
may correspond not only to visible light, but also to any
other electromagnetic wave such as ultraviolet, infrared,
microwaves, etc.)
Example
Suppose a particular lightbulb produces 10 watts (10
Joules/s) of red light with wavelength 663 nm. Each
photon has energy


6.63  10 34 3.00  10 8
19
E  hf 


3
.
00

10
J.

663  10 9
hc
So, to produce 10 J each second would require the
emission of
10
 3.33  1019 photons.
19
3.00  10
(Note that each photon releases a tiny “pulse” of light,
but with so many emissions each second, the resulting
light would appear “continuous”.)
The Photoelectric Effect
In the above example, matter (consisting of large numbers
of atoms) gives off light as a result of absorbing energy. It
turns out that matter can also emit charged particles
(electrons) by absorbing energy. This important
phenomenon is called the photoelectric effect.
Specifically, if you shine light of certain frequencies on
metals, they will emit electrons. (The mechanism here is
essentially that absorbed energy, in the form of photons,
can cause electrons previously held in the crystal lattice of
the metal to escape the metal altogether).
The photoelectric effect is the principle underlying the use
of photovoltaic cells, i.e. “solar cells”, which absorb
sunlight or other visible light and, through the release of
electrons, produce electric current which can be used to
operate switches, processors, motors, etc.
Note that the rate at which electrons are emitted has
much more to do with the frequency of the incident light
than its intensity. Light whose frequency is less than the
required minimum will produce no emissions whatsoever,
regardless of its brightness, whereas even very weak light
of sufficiently high frequency will produce some ejected
electrons.
Matter Waves
The discovery that light (initially shown to be a wave) can
be considered a particle soon led to the parallel discovery
that matter (i.e. particles) can also exhibit wave
behaviour. In other words, not only can waves act like
particles, but particles can act like waves!
The wavelike behaviour of matter is referred to as matter
waves, and is governed by the simple equation
h
h
 
p mv .
This equation can be applied to macroscopic (large scale)
objects, though it is only meaningful for subatomic
particles.
Example
For a 66.3 kg person walking at 1 m/s, the corresponding
matter wave would have a wavelength of
h
6.63 1034


 1035 m.
mv
66.31
Example
On the other hand, for a electron travelling at a (typical)
speed of 107 m/s,
h
6.63 1034
11
10



7
.
3

10

10
m.
mv 9.111031 107 
This is about the diameter of an atom.
Basically, these two examples suggest that the wavelength
of a matter wave can be thought of as the “region of
influence” of the matter itself. The region of influence
associated with a large-scale object is too small to make
any difference (i.e. to be detected or measured) while the
region of influence associated with an electron is (not
surprisingly) comparable to the size of an atom, whose
structure and behaviour is largely determined by the
presence of electrons!
The Uncertainty Principle
One of the most interesting ideas of quantum mechanics is
the uncertainty principle, first proposed by Heisenberg.
Essentially, this says that (at least for very small scale
objects) we can never know both a particle's location and
its momentum precisely. Rather, the more precisely you
know one, the less precisely you can know the other.
Mathematically, the uncertainty principle is expressed as
px  h .
This says that a reduction in the uncertainty in a body's
speed (i.e. uncertainty in its momentum) will be
accompanied by increased uncertainty in its location.
This isn't really a significant problem for large-scale
(macroscopic) bodies undergoing “everyday” motions,
since Planck's constant is so small that both momentum
and location can have very small uncertainties (and thus
both be known quite accurately).
Imagine trying to simultaneously determine the location
and momentum of a very tiny moving particle, however.
To detect the particle's position, a photon or electron must
instrument. Since the target is small, the momentum of
the photon or electron which interacts with it will actually
change the target particle's motion thereafter, slightly.
Furthermore, because it takes a finite (but small) amount
measuring instrument, it will no longer be at that location
by the time the measurement is complete. That is, the
very act of observing the particle changed its momentum,
and its actual location has also changed by the time the
measured location is recorded.
Applications of Quantum Mechanics
The applications of quantum theory in society today are
literally too many to list. The photoelectric effect is
responsible not only for the technology of photovoltaic
cells, but also for the physics behind transistors and other
semiconductors found in virtually all of today's electronic
devices. Matter wave theory is used in imaging devices
like electron microscopes, which use “electron waves”
rather than light waves.
The integrated circuits and microprocessor chips found in
today's computers and many other electronic instruments
can combine the equivalent of millions and even billions of
individual transistors within a very small space. Without
this ability to miniaturize electronic circuitry,
technologies like cell phones, MP3 players,
communication satellites and the space shuttle would all
have been impossible.
```