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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. 35533580. ISSN 13645021

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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 highprecision numerical calculations.
Item Type:  Journal Article 

Subjects:  Q Science > QC Physics 
Divisions:  Faculty of 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:  13645021 
Official Date:  8 November 2009 
Volume:  Vol.465 
Number:  No.2111 
Number of Pages:  28 
Page Range:  pp. 35533580 
Identification Number:  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) 
References:  [1] M. Berry. Histories of adiabatic quantum transitions. P Roy Soc Lond A Mat, 429(1876):61–72, Jan 
URI:  http://wrap.warwick.ac.uk/id/eprint/2462 
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