Variational Gaussian approximation for the magnetic Schrödinger equation

Selina Burkhard, Benjamin Dörich, Marlis Hochbruck, Caroline Lasser

Research output: Contribution to journalArticlepeer-review

Abstract

In the present paper we consider the semiclassical magnetic Schrödinger equation, which describes the dynamics of particles under the influence of a magnetic field. The solution of the time-dependent Schrödinger equation is approximated by a single Gaussian wave packet via the time-dependent Dirac-Frenkel variational principle. For the approximation we derive ordinary differential equations of motion for the parameters of the variational solution. Moreover, we prove L 2-error bounds and observable error bounds for the approximating Gaussian wave packet.

Original languageEnglish
Article number295202
JournalJournal of Physics A: Mathematical and Theoretical
Volume57
Issue number29
DOIs
StatePublished - 19 Jul 2024

Keywords

  • magnetic Schrödinger equation
  • observables
  • semiclassical analysis
  • variational approximation

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