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 generalize this approach and its recent enhancements to the magnetic Schrödinger equation for a time-dependent, spatially homogeneous magnetic field. 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.