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Tunneling dynamics and spawning with adaptive semi-classical wave-packets

by V. Gradinaru and G. A. Hagedorn and A. Joye

(Report number 2010-02)

Abstract
Tunneling through a one-dimensional Eckart barrier is investigated using a recently developed propagation scheme based on semi-classical wave-packets. This version of the time-dependent discrete variable representation method yields linear equations for the parameters, is fully adaptive, and does not require a frozen Ansatz in order to approximate the exact solution of the Schrödinger equation accurately. We rely on an analytical result to derive a new algorithm to spawn a second family of semi-classical wave-packets after the tunneling has occurred. Numerical results for a benchmark problem demonstrate the accuracy of the new method.

Keywords: semi-classical, time-dependent Schrödinger equation, wave-packets, tunneling, spawning, time-dependent discrete variable representation

@Techreport{GHJ10_424,
  author = {V. Gradinaru and G. A. Hagedorn and A. Joye},
  title = {Tunneling dynamics and spawning with adaptive semi-classical wave-packets},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2010-02},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2010/2010-02.pdf },
  year = {2010}
}

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