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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
BibTeX@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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