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Spawning Semiclassical Wavepackets

by O. Rietmann and V. Gradinaru

(Report number 2022-49)

Abstract
The semiclassical (or Hagedorn) wavepackets depending on a fixed set of parameters are an orthonormal \(L^{2}\)-basis of generalized coherent states. They have been used to solve numerically the time-dependent Schrödinger equation in its semiclassical formulation, yet their localization property makes them inefficient in case of non-local phenomena such as quantum tunneling. In order to overcome this difficulty, we use simultaneously a few members of several bases with different parameters. We propose an algorithm to expand a given wavefunction in terms of multiple families of Hagedorn wavepackets; each family can then be accurately and efficiently propagated using modern semiclassical time-splittings.

Keywords: quantum mechanics, Schrödinger equation, Hagedorn wavepackets, semiclassical, localization operator, signal analysis, machine learning

@Techreport{RG22_1037,
  author = {O. Rietmann and V. Gradinaru},
  title = {Spawning Semiclassical Wavepackets},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2022-49},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2022/2022-49.pdf },
  year = {2022}
}

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