Hagedorn wavepackets and Schrödinger equation with time-dependent, homogeneous magnetic field

Abstract

Certain generalized coherent states, so-called Hagedorn wavepackets, have been used to numerically solve the standard Schrödinger equation. We extend this approach and its recent enhancements to the magnetic Schrödinger equation for a time-dependent, spatially homogeneous magnetic field. We explain why Hagedorn wavepackets are naturally compatible with the aforementioned physical system. In numerical experiments we examine the order of convergence and the preservation of norm and energy. We use this method to simulate a Penning trap as proposed in recent work on quantum computing.