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

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

2008-01-21

arxiv.org/abs/0801.3246v6

Physics

Mathematical Physics

17 pages, no figures

Scientific paper

10.1007/s11005-008-0239-6

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.

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