dorsal/arxiv
View SchemaA New Method to Derive Low-Lying N-dimensional Quantum Wave Functions by Quadratures Along a Single Trajectory
| Authors | R. Friedberg, T. D. Lee, W. Q. Zhao |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0005039 |
| URL | https://arxiv.org/abs/quant-ph/0005039 |
| DOI | 10.1006/aphy.2000.6102 |
Abstract
We present a new method to derive low-lying N-dimensional quantum wave functions by quadrature along a single trajectory. The N-dimensional Schroedinger equation is cast into a series of readily integrable first order ordinary differential equations. Our approach resembles the familiar W.K.B. approximation in one dimension, but is designed to explore the classically forbidden region and has a much wider applicability than W.K.B.. The method also provides a perturbation series expansion and the Green's functions of the wave equation in N-dimension, all by quadratures along a single trajectory. A number of examples are given for illustration, including a simple algorithm to evaluate the Stark effect in closed form to any finite order of the electric field.
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"abstract": "We present a new method to derive low-lying N-dimensional quantum wave\nfunctions by quadrature along a single trajectory. The N-dimensional\nSchroedinger equation is cast into a series of readily integrable first order\nordinary differential equations. Our approach resembles the familiar W.K.B.\napproximation in one dimension, but is designed to explore the classically\nforbidden region and has a much wider applicability than W.K.B.. The method\nalso provides a perturbation series expansion and the Green\u0027s functions of the\nwave equation in N-dimension, all by quadratures along a single trajectory. A\nnumber of examples are given for illustration, including a simple algorithm to\nevaluate the Stark effect in closed form to any finite order of the electric\nfield.",
"arxiv_id": "quant-ph/0005039",
"authors": [
"R. Friedberg",
"T. D. Lee",
"W. Q. Zhao"
],
"categories": [
"quant-ph"
],
"doi": "10.1006/aphy.2000.6102",
"title": "A New Method to Derive Low-Lying N-dimensional Quantum Wave Functions by Quadratures Along a Single Trajectory",
"url": "https://arxiv.org/abs/quant-ph/0005039"
},
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