Propagator of a charged particle with a spin in uniform magnetic and perpendicular electric fields

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

Research output: Contribution to journalArticlepeer-review

38 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)159-178
Number of pages20
JournalLetters in Mathematical Physics
Volume84
Issue number2-3
DOIs
StatePublished - Jun 2008

Keywords

  • Forced harmonic oscillator
  • Fourier transform
  • Green function
  • Landau levels
  • Nonlinear Schrödinger equation
  • Propagator
  • Riccati differential equation
  • Schrödinger equation in electromagnetic field
  • The Cauchy initial value problem

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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