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

math-ph/0005006May 3, 2000

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 C (-γ/ε²), for some C and $γ>0$ .

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The paper addresses: A Time-Dependent Born-Oppenheimer Approximation with Exponentially Small Error Estimates.
We present the construction of an exponentially accurate time-dependent Born-Oppenheimer approximation for molecular quantum mechanics.