## 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