Propagator of a Charged Particle with a Spin in Uniform Magnetic and Perpendicular Electric Fields

TL;DR

This paper derives an explicit propagator for a spin-1/2 charged particle in uniform magnetic and perpendicular electric fields, providing a useful tool for quantum dynamics analysis in these conditions.

Contribution

It presents a new explicit solution for the time-dependent Schrödinger equation with combined magnetic and electric fields, including the Green function in elementary functions.

Findings

Explicit propagator expressed in elementary functions

Solution involves classical oscillator equations with time-dependent frequency

Discussion of special cases and nonlinear Schrödinger equation solutions

Abstract

We construct an explicit solution of the Cauchy initial value problem for the time-dependent Schroedinger equation for a charged particle with a spin moving in a uniform magnetic field and a perpendicular electric field varying with time. The corresponding Green function (propagator) is given in terms of elementary functions and certain integrals of the fields with a characteristic function, which should be found as an analytic or numerical solution of the equation of motion for the classical oscillator with a time-dependent frequency. We discuss a particular solution of a related nonlinear Schroedinger equation and some special and limiting cases are outlined.