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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

On variational approximations in quantum molecular dynamics


Author: Christian Lubich
Journal: Math. Comp. 74 (2005), 765-779
MSC (2000): Primary 65M15, 81Q05; Secondary 35Q40
Published electronically: May 25, 2004
MathSciNet review: 2114647
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Abstract | References | Similar Articles | Additional Information

Abstract: The Dirac-Frenkel-McLachlan variational principle is the basic tool for obtaining computationally accessible approximations in quantum molecular dynamics. It determines equations of motion for an approximate time-dependent wave function on an approximation manifold of reduced dimension. This paper gives a near-optimality result for variational approximations. It bounds the error in terms of the distance of the exact wave function to the approximation manifold and identifies the parameters that control the deviation of the variational approximation from the best approximation on the manifold.


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Additional Information

Christian Lubich
Affiliation: Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany
Email: lubich@na.uni-tuebingen.de

DOI: http://dx.doi.org/10.1090/S0025-5718-04-01685-0
PII: S 0025-5718(04)01685-0
Keywords: Quantum dynamics, Dirac-Frenkel-McLachlan variational principle, time-dependent Hartree and Hartree-Fock methods, optimality, error bounds
Received by editor(s): September 8, 2003
Published electronically: May 25, 2004
Article copyright: © Copyright 2004 American Mathematical Society