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 language | English (US) |
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Pages (from-to) | 159-178 |
Number of pages | 20 |
Journal | Letters in Mathematical Physics |
Volume | 84 |
Issue number | 2-3 |
DOIs | |
State | Published - 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