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Diagonalization of multicomponent wave equations with a Born-Oppenheimer example

Weigert, S. (orcid.org/0000-0002-6647-3252) and Littlejohn, Robert (1993) Diagonalization of multicomponent wave equations with a Born-Oppenheimer example. Physical Review A. pp. 3506-3512. ISSN 1094-1622

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A general method to decouple multicomponent linear wave equations is presented. First, the Weyl calculus is used to transform operator relations into relations between c-number valued matrices. Then it is shown that the symbol representing the wave operator can be diagonalized systematically up to arbitrary order in an appropriate expansion parameter. After transforming the symbols back to operators, the original problem is reduced to solving a set of linear uncoupled scalar wave equations. The procedure is exemplified for a particle with a Born-Oppenheimer-type Hamiltonian valid through second order in h. The resulting effective scalar Hamiltonians are seen to contain an additional velocity-dependent potential. This contribution has not been reported in recent studies investigating the adiabatic motion of a neutral particle moving in an inhomogeneous magnetic field. Finally, the relation of the general method to standard quantum-mechanical perturbation theory is discussed.

Item Type: Article
Copyright, Publisher and Additional Information: © 1993 The American Physical Society. Reproduced in accordance with the publisher's self-archiving policy.
Institution: The University of York
Academic Units: The University of York > Mathematics (York)
Depositing User: Repository Officer
Date Deposited: 23 Jun 2006
Last Modified: 13 Jun 2016 14:00
Published Version: http://dx.doi.org/10.1103/PhysRevA.47.3506
Status: Published
Refereed: Yes
URI: http://eprints.whiterose.ac.uk/id/eprint/1360

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