Conditions are established under which the Dirac equation for an electron in an electromagnetic field has an exact semiclassical solution. In other words, the phase is identified with a solution of the corresponding relativistic Hamilton-Jacobi equation and the spinor amplitude has no explicit dependence upon ℏ. The complete set of admissible fields is determined for one-dimensional and stationary three-dimensional systems, while an extensive class is indicated for the general time-dependent problem.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics