Relationship of quantum mechanics to classical electromagnetism and classical relativistic mechanics

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Some connections between quantum mechanics and classical physics are explored. The Planck–Einstein and De Broglie relations, the wavefunction and its probabilistic interpretation, the canonical commutation relations and the Maxwell–Lorentz equation may be understood in a simple way by comparing classical electromagnetism and the photonic description of light provided by classical relativistic kinematics. The method used may be described as ‘inverse correspondence’ since quantum phenomena become apparent on considering the low photon number density limit of classical electromagnetism. Generalization to massive particles leads to the Klein–Gordon and Schrödinger equations. The difference between the quantum wavefunction of the photon and a classical electromagnetic wave is discussed in some detail.