Quantum Theory

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PH103
Quantum Theory
Dr. James van Howe Lecture 18
April 28, 2008
Max Planck, father of Quantum Theory
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I think it is safe to say that no one
understands quantum mechanics
-Richard Feynman
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Brief History of Quantum

• 1900 Max Planck introduces quantum theory to
  explain thermal radiation
• 1905 Einstein introduces concept of the photon
  to explain the photoelectric effect
• 1909 Millikan oil drop experiment, quantization
  of charge
• 1913 Niels Bohr introduces quantum model of atom
• 1916 Millikan experimentally verifies
  photoelectric effect
• 1924 Louis de Broglie postulates wave behavior
  of matter
• 1926 Schrodinger introduces wave (quantum)
  mechanics
• Max Born establishes probabilistic
  interpretation of wave functions
• 1927 Werner Heisenberg develops uncertainty
  principle

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When you think Quantum, think

• Discrete (digital), not continuous
• Probability, Probabilistic
• Waves, wave function (probability wave)

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Blackbody Radiation
Everything emits electromagnetic radiation just
by having a nonzero temperature
If you heat up a piece of metal very hot it
glows it gives off light which is an
electromagnetic wave.
Even objects not hot enough to glow, still give
off EM waves. Like you (though you need special
detector to see them)
From LAND, infrared thermal imaging
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Why the name blackbody?
Technically we are concerned only with thermal
radiation. We dont want any reflections from the
surface to skew our results. If the object is
green, we will think it is emitting green
radiation, but really it is just reflecting the
green portion of light. If we make it black, we
wont get any reflection from the surface at all.
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More Pickiness
We also need the blackbody to be a cavity, like a
box, with a small opening. Why? This way stray
radiation that gets in will be trapped inside and
have a low probability of getting out. On the
other hand, the radiation coming out of the hole
will be almost the pure thermal radiation from
the blackbody that we want to detect.
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Modes of a Cavity
There are many EM waves inside the box, but the
ones we detect at the hole are only those that
constructively interfere (standing waves).
This is like sound waves in a violin or a guitar
Interference holography shows the cavity modes of
the violin
A mode is just an allowed wave.
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Remember modes on a string (one-dimensional
cavity)?
L
l/2
l
3l/2
In general
Infinite number of modes, but only at certain
frequencies
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Thermodynamics and Probability
In 1877 Boltzmann found that a group of particles
at an average temperature T has a probable range
of energies
The probability between 0 and 1 of energy E,
given a temperature T is
E is energy, A is a constant, T is temperature, k
is Boltzmanns constant
The higher E, the lower the probability the mode
exists. The less intense the radiation. Most
probable energies are below kT.
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L
l/2
l


Classically Each mode has an Energy kT, and so
the energy of each mode (each frequency) is
equally probable. Probability does not depend on
frequency.
If we have modes n1 through n 5, the then the
intensity of radiation if proportional to 5.
If we have modes n1 through n infinity, Total
Intensity is infinity. Not true though!
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UV Catastrophe
So classically as you have more modes (more
frequency), the intensity keeps going up
indefinitely!
Doesnt happen in real life, but it peaks at
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Papa Planck Solves the UV catastrophe
Planks quantum theory said that the energy for
the blackbody radiation comes in discrete steps
(quanta)
Where Plancks constant
Since each mode of the cavity is simply
Therefore the probability of high frequency modes
existing is much less than those of lower
frequency
Now probability depends on frequency of mode.
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Another way to say it

• Planks theory
• Light must be given off as individual photons (he
  didnt use that term)
• Each has energy E hf.
• High frequency light made up of high energy
  photons.
• Requires a lot of energy to produce one.
• Harder to produce, so probabilistically less
  likely to be produced.
• In fact as f??, E??
• not just unlikely, impossible to produce one
• power spectrum goes to zero as f??

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Black Body Spectrum
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Common Sense Part
If you have a a fire, which color is hotter (has
more energy), a red flame or a blue flame?
Blue flame
Blue is higher in frequency than red, so by
quantum theory, the energy should be higher too.
Checks out
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Photo-electric effect
In the same year that Einstein published his work
on special relativity, 1905, took Plancks
quantum theory a step further.
Einstein said that quantized energy of EM
radiation, actually corresponded to discrete
packets of energy called photons
Photons were to be thought of as massless
particles of light whose energy is described by
Recall from relativity
so
If correct, light therefore should exhibit
particle-like behavior
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Einstein proposed the photoelectric effect, which
was verified experimentally in 1916 by Millikan

• Light strikes a metal, knocking electrons off the
  metal surface.
• Light energy converted to electrical energy.

• The electrons could absorb energy from a wave or
  a particle of light
• but wave theory cant explain the details...
• Particle (photon) theory can

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Photoelectric Effect Detail 1

• If lights frequency is below a critical
  frequency, fltfc,
• then the photoelectric effect doesn't happen
• Classical wave theory of light cannot explain why
  frequency should affect it.
• Photon theory (with Ehf) can
• Low frequency means low energy.
• If fltfc, then the energy of the photon is too low
  to free the electron from the metal.
• F energy needed to free electron
• For effect to occur hf gt F

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Photoelectric Effect Detail 2
The kinetic energy of the ejected electrons
increases with the frequency of the light
K
Slopeh
f
fc
No effect
-F
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Photoelectric Effect Detail 2

• When the effect does occur, increasing the
  frequency of the light increases the kinetic
  energy of the electrons that are released
• Again classical wave theory cannot explain why
  frequency should matter.
• Only intensity predicted to affect energy.
• Again photon theory can
• photons energy, hf, is absorbed by electron,
• some energy is used to free electron,
• rest of energy is kinetic energy.