Invariant Solution of Dirac Equation in Crossed Electric and Magnetic Fields. Spin Integral of Motion. (H < E)

Abstract

In this paper analytic and invariant solution of the electron motion in crossed electric and magnetic fields where H < E is examined. It is shown that the invariant solution of the proposed problem is formally similar to that of quantum harmonic oscillator. Examining the polarity operator in external field, it is deduced that there is an expression consisting of spin components which remains constant throughout the motion and therefore is integral of motion. Eigenvalues and eigenfunctions corresponding to spin integral of motion are found and analyzed.