00-209 George A. Hagedorn, Alain Joye

A Time--Dependent Born--Oppenheimer Approximation with Exponentially Small Error Estimates (118K, Latex 2e) May 3, 00

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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 $\epsilon^{-4}$, where $\epsilon$ is a small expansion parameter. By optimal truncation of an asymptotic expansion, we construct approximate solutions to the time--dependent Schr\"odinger equation that agree with exact normalized solutions up to errors whose norms are bounded by $\ds C\,\exp\left(\,-\gamma/\epsilon^2\,\right)$, for some $C$ and $\gamma>0$.

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