Time-integration of Gaussian variational approximation for the magnetic Schrödinger equation

In the present paper we consider the semiclassical magnetic Schrödinger equation, which describes the dynamics of charged particles under the influence of an electro-magnetic field. The solution of the time-dependent Schrödinger equation is approximated by a single Gaussian wave packet via the time-...

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Bibliographic Details
Published in:Journal of computational physics Vol. 541; p. 114349
Main Authors: Scheifinger, Malik, Busch, Kurt, Hochbruck, Marlis, Lasser, Caroline
Format: Journal Article
Language:English
Published: Elsevier Inc 05.11.2025
Subjects:
Boris algorithm
Gaussian wave packets
Mesh-free method
Penning trap
Runge–Kutta
Semiclassical magnetic Schrödinger equation
Time-dependent variational approximation
Gaussian wave packets
81-08
81Q05
Time-dependent variational approximation
Boris algorithm
Runge–Kutta
37M15
78M30
Penning trap
81Q20
Mesh-free method
Semiclassical magnetic Schrödinger equation
ISSN:0021-9991
Online Access:Get full text
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Summary:In the present paper we consider the semiclassical magnetic Schrödinger equation, which describes the dynamics of charged particles under the influence of an electro-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 use ordinary differential equations of motion for the parameters of the variational solution and extend the second-order Boris algorithm for classical mechanics to the quantum mechanical case. In addition, we propose a modified version of the classical fourth-order Runge–Kutta method. Numerical experiments explore parameter convergence and geometric properties. Moreover, we benchmark against the analytical solution of the Penning trap.
ISSN:0021-9991
DOI:10.1016/j.jcp.2025.114349