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

Preprint

28 January 2008

preprint
Published by arXiv in arXiv

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 an 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. A particular solution of a related nonlinear Schroedinger equation is discussed. Some special and limiting cases are outlined.

Keywords

PERPENDICULAR ELECTRIC
SCHROEDINGER EQUATION
INITIAL VALUE PROBLEM
NUMERICAL SOLUTION
CHARGED PARTICLE
UNIFORM MAGNETIC
ELECTRIC FIELDS
PROPAGATOR

All Related Versions

Version 1, 2008-01-21, ArXiv
Version 2, 2008-01-23, ArXiv
Version 3, 2008-01-28, ArXiv
Version 4, 2008-01-30, ArXiv
Version 5, 2008-01-31, ArXiv
Published version: Letters in Mathematical Physics, 84 (2-3), 159.

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