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