A time-dependent Born-Oppenheimer approximation with exponentially small error estimates. (English) Zbl 1161.81376
Summary: 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 \(\varepsilon^{-4}\), where \(\varepsilon\) 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 \(C\exp(-\gamma/\varepsilon^2)\), for some \(C\) and \(\gamma >0\).
MSC:
81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
81Q20 | Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory |
81V55 | Molecular physics |