dorsal/arxiv
View SchemaStationary Perturbation Theory with Spatially Well-separated Potentials
| Authors | Seok Kim, Choonkyu Lee |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0209046 |
| URL | https://arxiv.org/abs/quant-ph/0209046 |
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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"abstract": "We present a new perturbation theory for quantum mechanical energy\neigenstates when the potential equals the sum of two localized, but not\nnecessarily weak potentials $V_{1}(\\vec{r})$ and $V_{2}(\\vec{r})$, with the\ndistance $L$ between the respective centers of the two taken to be quite large.\nIt is assumed that complete eigenfunctions of the local Hamiltonians (i.e., in\nthe presence of $V_{1}(\\vec{r})$ or $V_{2}(\\vec{r})$ only) are available as\ninputs to our perturbation theory. If the two local Hamiltonians have\ndegenerate bound-state energy levels, a systematic extension of the molecular\norbital theory (or the tight-binding approximation) follows from our formalism.\nOur approach can be viewed as a systematic adaptation of the multiple\nscattering theory to the problem of bound states.",
"arxiv_id": "quant-ph/0209046",
"authors": [
"Seok Kim",
"Choonkyu Lee"
],
"categories": [
"quant-ph",
"hep-th"
],
"title": "Stationary Perturbation Theory with Spatially Well-separated Potentials",
"url": "https://arxiv.org/abs/quant-ph/0209046"
},
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