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arXiv · 2310.16734

Variational Gaussian approximation for the magnetic Schr\"odinger equation

Selina Burkhard·Benjamin Dörich·Marlis Hochbruck·Caroline Lasser
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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 $L^2$-error bounds and observable error bounds for the approximating Gaussian wave packet.

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Selina Burkhard, Benjamin Dörich, Marlis Hochbruck, Caroline Lasser. 2023-10-25. Variational Gaussian approximation for the magnetic Schr\"odinger equation. https://arxiv.org/abs/2310.16734

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