 00209 George A. Hagedorn, Alain Joye
 A TimeDependent BornOppenheimer Approximation with Exponentially
Small Error Estimates
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May 3, 00

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Abstract. We present the construction of an exponentially accurate timedependent
BornOppenheimer 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
timedependent 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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