Quantum Mechanical Motion of an Electron in Inhomogeneous Electric and Magnetic Fields

Abstract

Dirac equation governs the behavior of relativistic motion of spin ½ particles. Several instances of solution of Dirac equation in various field configurations can be seen in the literature. In this paper we present certain exact solutions of the Dirac equation for an electron in crossed inhomogeneous electric and magnetic fields. Closed form bound state solutions are obtained in terms of Laguerre polynomials. The eigenvalues reduce to the results in the literature in the limit of vanishing inhomogeneity and electric field.

Keywords: Bound State Solutions, Dirac Equation, Inhomogeneous Fields, Kratzer’s Molecular, Laguerre Polynomials