Classical vs Quantum Electromagetism

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SUMMARY

The discussion centers on the relationship between classical electromagnetism, as described by Maxwell's equations, and quantum electrodynamics (Q.E.D.). It establishes that a classical electromagnetic wave can be viewed as a collection of a large number of coherent photons, where the electric (E) and magnetic (B) field components are derived from the quantum mechanical four-potential Aμ of a photon. This relationship highlights the transition from classical to quantum descriptions of electromagnetic radiation.

PREREQUISITES
  • Maxwell's equations for classical electromagnetism
  • Quantum electrodynamics (Q.E.D.) principles
  • Understanding of coherent states in quantum mechanics
  • Familiarity with the four-potential Aμ in quantum field theory
NEXT STEPS
  • Study the derivation of electromagnetic waves from Maxwell's equations
  • Explore the concept of coherent photons in quantum mechanics
  • Learn about the mathematical formulation of quantum electrodynamics (Q.E.D.)
  • Investigate the implications of the four-potential Aμ in electromagnetic theory
USEFUL FOR

Physicists, electrical engineers, and students of advanced electromagnetism seeking to deepen their understanding of the interplay between classical and quantum theories of electromagnetic radiation.

LarryS
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I'm having trouble relating the classical (Maxwell) model for electromagnetic radiation to the quantum mechanical (Q.E.D.) model. How do the magnetic field wave and electic field wave components of the classical electromagnetic wave relate to the quantum mechanical wave function for a photon?
 
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E and B are found from the QM A^\mu of a photon using the usual classical definitions.
A classical EM wave corresponds to N coherent photons, with N>>>1.
 

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