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

TL;DR

This paper develops a semiclassical approximation method for high-energy electrons in a magnetic field, linking quantum solutions to classical charge motion and spin precession through superposition of energy states.

Contribution

It introduces a procedure using exact Klein-Gordon and Dirac-Pauli solutions to connect quantum states with classical equations for high-energy electrons in magnetic fields.

Findings

Quantum states are represented as superpositions of neighboring energy levels.

Expectation values of momentum and spin follow classical equations.

The method effectively bridges quantum and classical descriptions for high-energy particles.

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.