A Time-Dependent Born–Oppenheimer Approximation with Exponentially Small Error Estimates
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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.
KeywordsError Estimate Quantum Mechanic Approximate Solution Asymptotic Expansion Molecular System
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