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Quantum physics
Ch. 12
Quantum physics can be traced to a single concept:
Each particle is associated with a wave and vice versa.
These are two different aspects of the same object.
For example, an electromagnetic wave is associated
with a particle, the photon.
The puzzle will be resolved by introducing the concept
of a wave packet (called wave function in physics):
The wave packet determines the probability of finding
the particle.
Probability in quantum physics
The wave packet determines the probability of finding the particle.
Buildup of
a diffraction
pattern from
individual
photons.
Number of
of a light wave
= Probability of finding a photon
Consequences of the particle/wave concept
1) The Quantum
– The energy of a wave takes discrete values (quanta),
because a wave consists of discrete particles.
– For example, a laser beam consists of many photons,
each carrying the same photon energy.
2) Probabilities
– One cannot predict exactly how an individual particle
will behave. The probability can be obtained from the
intensity of the wave packet.
– Accurate results can be obtained after repeating the
same experiment with many particles and averaging.
3) The Uncertainty Relation
– There is a tradeoff between particle and wave character.
– Depending on the width of the wave packet, an object can
be more like a particle or like a wave.
– A particle (short wave packet) has a well-defined position,
and a wave (long packet) has a well-defined momentum.
– That leads to a tradeoff between the uncertainties in the
position and the momentum.
These results will be fleshed out in the following lectures.
Fortunately, the strange rules of quantum
physics affect only very small objects,
such as individual atoms and electrons.
As soon as we have a macroscopic object
consisting of many atoms, an experiment
becomes more predictable.
Typically, a macroscopic object consists of 1024
atoms (Avogadro’s number). Averaging over
1024 atoms reduces the statistical error to
1/1024 = 1/1012 = 1 in a trillion.
Relativity makes the result of a measurement
dependent on the observer.
Quantum physics goes farther and makes a
measurement on a single particle uncertain.
Special relativity: Important for high velocities
General relativity: Important for strong gravity
Quantum physics: Important for small objects
Origins of quantum physics
Planck found that the radiation from a
glowing object can be explained only
by assuming that energy is radiated in
discrete quanta. The size of an energy
quantum is:
E = h· f
E = Energy of a particle
f = Frequency of a wave
h = Planck’s constant
ħ= h
2
Waves as Particles
Einstein explained emission of
electrons from a solid by light
in 1905, using the concept of
light particles = photons .
The energy of a photon is:
E = h· f
Nothing happens if the energy of
the photons is too low (red light).
He later received his Nobel prize
for this work (not for relativity!).
Particles as Waves
54 eV
electrons
DeBroglie predicted that
particles should behave
like waves.
Davisson and Germer
observed that electrons
are diffracted by a nickel
crystal.
This is analogous to the
diffraction of light waves
(Lecture 9).
 = 0.17 nm
Bright spots:
Interference
pattern
Generalization:
Every particle is a wave, and vice versa
Particle properties:
Energy E
Wave properties:
E = h/T
Period in time = T = 1/f
(Planck)
Momentum p
p = h/ 
Period in space = 
(de Broglie)
(Compare waves, Lect. 8, Slide 4)
Equations for waves
Electron waves are described by the
Schrödinger equation .
(Erwin Schrödinger 1926)
Its relativistic generalization is the
Dirac equation.
(Paul Dirac 1928)
Photon waves (electromagnetic waves)
are described by Maxwell’s equations.
Although Maxwell’s equations appeared decades
before relativity and quantum physics, they are
perfectly compatible with these new theories.
That is one more reason why physicists are fond
of them. Mathematical elegance proved to be a
good criterion for correct physics.
The equations of general relativity are also very
elegant, but incompatible with quantum theory.
String theorists have quite elegant equations for
quantum gravity, but these are not testable.