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Stationary Perturbation Theory with Spatially Well-separated Potentials

Seok Kim·Choonkyu Lee
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Abstract

We present a new perturbation theory for quantum mechanical energy eigenstates when the potential equals the sum of two localized, but not necessarily weak potentials $V_{1}(\vec{r})$ and $V_{2}(\vec{r})$, with the distance $L$ between the respective centers of the two taken to be quite large. It is assumed that complete eigenfunctions of the local Hamiltonians (i.e., in the presence of $V_{1}(\vec{r})$ or $V_{2}(\vec{r})$ only) are available as inputs to our perturbation theory. If the two local Hamiltonians have degenerate bound-state energy levels, a systematic extension of the molecular orbital theory (or the tight-binding approximation) follows from our formalism. Our approach can be viewed as a systematic adaptation of the multiple scattering theory to the problem of bound states.

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Seok Kim, Choonkyu Lee. 2002-09-06. Stationary Perturbation Theory with Spatially Well-separated Potentials. https://arxiv.org/abs/quant-ph/0209046

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