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

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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 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.

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Received: 13 February 2001 / Accepted: 13 July 2001

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Hagedorn, G., Joye, A. A Time-Dependent Born–Oppenheimer Approximation with Exponentially Small Error Estimates. Commun. Math. Phys. 223, 583–626 (2001). https://doi.org/10.1007/s002200100562

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  • DOI: https://doi.org/10.1007/s002200100562

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