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Communications in Mathematical Physics

, Volume 223, Issue 3, pp 583–626 | Cite as

A Time-Dependent Born–Oppenheimer Approximation with Exponentially Small Error Estimates

  • George A. Hagedorn
  • Alain Joye

Abstract:

We present the construction of an exponentially accurate time-dependent Born–Oppenheimer approximation for molecular quantum mechanics.

We study molecular systems whose electron masses are held fixed and whose nuclear masses are proportional to ε−4, where ε is a small expansion parameter. By optimal truncation of an asymptotic expansion, we construct approximate solutions to the time-dependent Schrödinger equation that agree with exact normalized solutions up to errors whose norms are bounded by \(\), for some C and γ >0.

Keywords

Error Estimate Quantum Mechanic Approximate Solution Asymptotic Expansion Molecular System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • George A. Hagedorn
    • 1
  • Alain Joye
    • 2
  1. 1.Department of Mathematics and Center for Statistical Mechanics and Mathematical Physics, Virginia¶Polytechnic Institute and State University, Blacksburg, Virginia 24061-0123, USAUS
  2. 2.Institut Fourier, Unité Mixte de Recherche CNRS-UJF 5582, Université de Grenoble I, BP 74,¶38402 Saint Martin d'Hères Cedex, FranceFR

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