## Source-Free Classical Electromagnetism, the Free-Photon Schroedinger Equation, and the Unphysical Conjugate-Pair Solutions of the Klein-Gordon and Dirac Equations

**Authors:** Steven Kenneth Kauffmann

This tutorial begins with the relationship of source-free classical electromagnetism to ultra-relativistic free-photon quantum mechanics. The linear transformation of the source-free classical-electromagnetic real-valued transverse vector potential to its corresponding free-photon Schroedinger-equation complex-valued transverse vector wave function is obtained. It is then pointed out that despite the free-photon Klein-Gordon equation's being formally identical to the source-free classical-electromagnetic vector-potential wave equation, it yields not only free-photon Schroedinger-equation wave functions but also their complex conjugates, which don't satisfy the free-photon Schroedinger equation. This is a consequence of admitting complex-valued solutions of the Klein-Gordon equation -- of course only its real-valued solutions apply to the classical vector potential. It is pointed out that solutions of the free-particle Dirac equation likewise occur in conjugate pairs, and that its Hamiltonian operator implies a variety of unphysical consequences, e.g., any Dirac free particle's speed is that of light times the square root of three.

**Comments:** 4 Pages.

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### Submission history

[v1] 2019-03-21 18:36:43

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