A classical derivation of Dirac's Equation

Bernard H. Lavenda

Hans Sallhofer

As is well known, the Schrödinger equation can be derived by suitably arranging the refraction in the classical equation for light inhomogeneous media. In this paper it is shown that one may derive the Dirac equation in complete analogy by arranging for the refraction in the electrodynamics of inhomogeneous media.

Iwo Białynicki‐Birula, Zofia Białynicka-Birula

Abstract We introduce a new method to derive solutions of the Dirac equation in external static fields that have a direct connection to classical physics. Using it, we derive new analytic solutions of the Dirac equation in a magnetic field, which reproduce the motion of relativistic classical particles. We also generalize this method to the case of crossed electric and magnetic field.

Frank A. Wilczek

Miroslav Pardy

The equivalent system of equations corresponding to the Dirac equation is derived and the WKB approximation of this system is found. Similarly, the WKB approximation for the equivalent system of equation corresponding to the squared Dirac equation is found and it is proved that the Lorentz equation and the Bargmann-Michel-Telegdi iquations follow from the new Dirac-Pardy system. The new tensor equation with sigma matrix is derived for the verification by adequate laboratories.