dorsal/arxiv
View SchemaGreen functions for generalized point interactions in 1D: A scattering approach
| Authors | Alexandre G. M. Schmidt, Bin Kang Cheng, Marcos G. E. da Luz |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0211193 |
| URL | https://arxiv.org/abs/quant-ph/0211193 |
| DOI | 10.1103/PhysRevA.66.062712 |
Abstract
Recently, general point interactions in one dimension has been used to model a large number of different phenomena in quantum mechanics. Such potentials, however, requires some sort of regularization to lead to meaningful results. The usual ways to do so rely on technicalities which may hide important physical aspects of the problem. In this work we present a new method to calculate the exact Green functions for general point interactions in 1D. Our approach differs from previous ones because it is based only on physical quantities, namely, the scattering coefficients, $R$ and $T$, to construct $G$. Renormalization or particular mathematical prescriptions are not invoked. The simple formulation of the method makes it easy to extend to more general contexts, such as for lattices of $N$ general point interactions; on a line; on a half-line; under periodic boundary conditions; and confined in a box.
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"abstract": "Recently, general point interactions in one dimension has been used to model\na large number of different phenomena in quantum mechanics. Such potentials,\nhowever, requires some sort of regularization to lead to meaningful results.\nThe usual ways to do so rely on technicalities which may hide important\nphysical aspects of the problem. In this work we present a new method to\ncalculate the exact Green functions for general point interactions in 1D. Our\napproach differs from previous ones because it is based only on physical\nquantities, namely, the scattering coefficients, $R$ and $T$, to construct $G$.\nRenormalization or particular mathematical prescriptions are not invoked. The\nsimple formulation of the method makes it easy to extend to more general\ncontexts, such as for lattices of $N$ general point interactions; on a line; on\na half-line; under periodic boundary conditions; and confined in a box.",
"arxiv_id": "quant-ph/0211193",
"authors": [
"Alexandre G. M. Schmidt",
"Bin Kang Cheng",
"Marcos G. E. da Luz"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.66.062712",
"title": "Green functions for generalized point interactions in 1D: A scattering approach",
"url": "https://arxiv.org/abs/quant-ph/0211193"
},
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