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

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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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Authors and Affiliations

  1. Department of Mathematics and Statistics, Arizona State University, Tempe, AZ, 85287–1804, USA

    Ricardo Cordero-Soto, Raquel M. Lopez, Erwin Suazo & Sergei K. Suslov

Authors
  1. Ricardo Cordero-Soto
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  2. Raquel M. Lopez
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  3. Erwin Suazo
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  4. Sergei K. Suslov
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Corresponding author

Correspondence to Sergei K. Suslov.

Additional information

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

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