Abstract
We construct an explicit solution of the Cauchy initial value problem for the time-dependent Schrödinger 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 Schrödinger equation and some special and limiting cases are outlined.
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We dedicate this paper to the memory of Professor Basil Nicolaenko for his significant contributions to the area of nonlinear partial differential equations, applied mathematics, and related topics.
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Cordero-Soto, R., Lopez, R.M., Suazo, E. et al. Propagator of a Charged Particle with a Spin in Uniform Magnetic and Perpendicular Electric Fields. Lett Math Phys 84, 159–178 (2008). https://doi.org/10.1007/s11005-008-0239-6
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DOI: https://doi.org/10.1007/s11005-008-0239-6