dorsal/arxiv
View SchemaMinimax determination of the energy spectrum of the Dirac equation in a Schwarzschild background
| Authors | Alejandro Caceres, Chris Doran |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0503042 |
| URL | https://arxiv.org/abs/quant-ph/0503042 |
| DOI | 10.1103/PhysRevA.72.022103 |
Abstract
We calculate the bound-state energy spectrum of the Dirac Equation in a Schwarzschild black hole background using a minimax variational method. Our method extends that of Talman to the case of non-Hermitian interactions, such as a black hole. The trial function is expressed in terms of a basis set that takes into account both the Hermitian limit of the interaction in the non-relativistic approximation, and the general behaviour of the solutions at the origin, the horizon and infinity. Using this trial function an approximation to the full complex energy bound-state spectrum is computed. We study the behaviour of the method as the coupling constant of the interaction is increased, which increases both the relativistic effects and the size of the non-Hermitian part of the interaction. Finally we confirm that the method follows the expected Hylleraas-Undheim behaviour.
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"abstract": "We calculate the bound-state energy spectrum of the Dirac Equation in a\nSchwarzschild black hole background using a minimax variational method. Our\nmethod extends that of Talman to the case of non-Hermitian interactions, such\nas a black hole. The trial function is expressed in terms of a basis set that\ntakes into account both the Hermitian limit of the interaction in the\nnon-relativistic approximation, and the general behaviour of the solutions at\nthe origin, the horizon and infinity. Using this trial function an\napproximation to the full complex energy bound-state spectrum is computed. We\nstudy the behaviour of the method as the coupling constant of the interaction\nis increased, which increases both the relativistic effects and the size of the\nnon-Hermitian part of the interaction. Finally we confirm that the method\nfollows the expected Hylleraas-Undheim behaviour.",
"arxiv_id": "quant-ph/0503042",
"authors": [
"Alejandro Caceres",
"Chris Doran"
],
"categories": [
"quant-ph",
"gr-qc"
],
"doi": "10.1103/PhysRevA.72.022103",
"title": "Minimax determination of the energy spectrum of the Dirac equation in a Schwarzschild background",
"url": "https://arxiv.org/abs/quant-ph/0503042"
},
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