Quantum Theory of Light

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Quantum Theory of Light

• Classical Creation Theory

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Differential Forms
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Wave Equation
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Blackbody Radiation

• Closed Box with a tiny pinhole
• Inside is heated by emission from the inside
  walls. Eventually, the inside will attain the
  same temperature as the outside.
• Radiation from the pinhole is called Blackbody
  Radiation
• A perfect radiator absorbs all radiation falling
  on it that is why it is called a black body.

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Blackbody Radiation Laws

• Kirchhoffs Theorem
• Energy emitted at a frequency f depends only on
  the frequency and the temperature.
• Stefans Law
• Total power per unit area emitted at ALL
  frequencies is proportional to the fourth power
  of absolute temperature.

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Blackbody Radiation Laws
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Spectral Energy Density

• We have considered the power radiated per unit
  area per unit frequency J(f,T).
• Next consider energy per unit volume per unit
  frequency within the Blackbody, u(f,T).
• The two must be proportional
• By averaging over direction the constant of
  proportionality is just c/4.

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Wiens Exponential Law

• Wein guessed that the universal function u(f,T)
  had the form

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Plancks Version

• Plank knew that Weins Law worked fine at short
  wavelengths. He tried to derive the law using
  statistical mechanics and Maxwells Laws.
  Nothing worked.
• He learned that for long wavelengths that u(f,T)
  was proportional to T.

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Plancks Version

• New empirical formula

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Plancks Version

• So what is the explanation for h?
• Billions of resonators in the walls of the
  cavity vibrating at different frequencies
• Total energy of a resonator could only be an
  integral multiple of hf

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Plancks Version

• Resonators at multiple frequencies with emission
  at individual frequencies
• Equilibrium between resonators and radiation in
  the cavity

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Plancks Version

• So, now we have to compute the average energy per
  oscillator
• Classically, radiation in the cavity is standing
  waves with temperature T
• According to Boltzmann, average energy must be
  proportional to T for a degree of freedom
• Compare to ideal gas law!

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Plancks Version
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Plancks Version

• Quantize the energy of the standing waves

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Plancks Version
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Plancks Version

• Assumptions, energynhf
• Change in energy is hf