Verification of the semiclassical method for an electron moving in a homogeneous magnetic field

Abstract

A procedure based on the semiclassical approximation for high energy levels is developed to yield solutions to the classical equation of charge motion and to the Bargmann-Michel-Telegdi spin equation. To this end, exact solutions to the Klein-Gordon and the Dirac-Pauli equations are used. The essence of the procedure under review is that the quantum state of a charged particle in a homogeneous magnetic field is represented as a superposition of states corresponding to the neighboring energy levels. As a consequence, the behavior of the expectation values of the momentum and spin operators with respect to the resulting nonstationary wave function (packet) strictly obey the classical equations of charge motion and spin precession.