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Superadiabatic transitions in quantum molecular dynamics
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Betz, Volker, Goddard, B. and Teufel, Stefan (2009) Superadiabatic transitions in quantum molecular dynamics. Proceedings of the Royal Society of London. A, Mathematical, Physical and Engineering Sciences, Vol.465 (No.2111). pp. 3553-3580. doi:10.1098/rspa.2009.0337 ISSN 1364-5021.
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Official URL: http://dx.doi.org/10.1098/rspa.2009.0337
Abstract
We study the dynamics of a molecule’s nuclear wave function near an avoided crossing of two electronic energy levels for one nuclear degree of freedom. We derive the general form of the Schrödinger equation in the nth superadiabatic representation for all n є N. Using these results, we obtain closed formulas for the time development of the component of the wave function in an initially unoccupied energy subspace when a wave packet travels through the transition region. In the optimal superadiabatic representation, which we define, this component builds up monotonically. Finally, we give an explicit formula for the transition wave function away from the avoided crossing, which is in excellent agreement with high-precision numerical calculations.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QC Physics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Quantum theory -- Mathematical models, Wave functions, Schrödinger equation, Eigenvalues | ||||
Journal or Publication Title: | Proceedings of the Royal Society of London. A, Mathematical, Physical and Engineering Sciences | ||||
Publisher: | The Royal Society Publishing | ||||
ISSN: | 1364-5021 | ||||
Official Date: | 8 November 2009 | ||||
Dates: |
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Volume: | Vol.465 | ||||
Number: | No.2111 | ||||
Number of Pages: | 28 | ||||
Page Range: | pp. 3553-3580 | ||||
DOI: | 10.1098/rspa.2009.0337 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC) | ||||
Grant number: | EP/D07181X/1 (EPSRC) |
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