Variational Gaussian approximation for the magnetic Schr\"odinger equation
Numerical Analysis
2023-10-26 v1 Numerical Analysis
Mathematical Physics
math.MP
Abstract
In the present paper we consider the semiclassical magnetic Schr\"odinger equation, which describes the dynamics of particles under the influence of a magnetic field. The solution of the time-dependent Schr\"odinger 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 -error bounds and observable error bounds for the approximating Gaussian wave packet.
Cite
@article{arxiv.2310.16734,
title = {Variational Gaussian approximation for the magnetic Schr\"odinger equation},
author = {Selina Burkhard and Benjamin Dörich and Marlis Hochbruck and Caroline Lasser},
journal= {arXiv preprint arXiv:2310.16734},
year = {2023}
}