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

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 Schrödinger equation that agree with exact normalized solutions up to errors whose norms are bounded by $\ds C \exp(-γ/ε^2)$, for some C and $\gamma >0$.

References in corpus (1)

• Semiclassical Dynamics with Exponentially Small Error Estimates

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