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Hagedorn Wavepackets and Schrödinger Equation with Time-Dependent, Homogeneous Magnetic Field

by V. Gradinaru and O. Rietmann

(Report number 2020-68)

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.

Keywords: Hagedorn wavepackets, Schrödinger equation, magnetic field, splitting, perturbation, Penning trap

@Techreport{GR20_941,
  author = {V. Gradinaru and O. Rietmann},
  title = {Hagedorn Wavepackets and Schr\"odinger Equation with Time-Dependent, Homogeneous Magnetic Field},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2020-68},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2020/2020-68.pdf },
  year = {2020}
}

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