dorsal/arxiv
View SchemaKepler problem in Dirac theory for a particle with position-dependent mass
| Authors | I. O. Vakarchuk |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0502105 |
| URL | https://arxiv.org/abs/quant-ph/0502105 |
| DOI | 10.1088/0305-4470/38/21/016 |
Abstract
Exact solution of Dirac equation for a particle whose potential energy and mass are inversely proportional to the distance from the force centre has been found. The bound states exist provided the length scale $a$ which appears in the expression for the mass is smaller than the classical electron radius $e^2/mc^2$. Furthermore, bound states also exist for negative values of $a$ even in the absence of the Coulomb interaction. Quasirelativistic expansion of the energy has been carried out, and a modified expression for the fine structure of energy levels has been obtained. The problem of kinetic energy operator in the Schr\"odinger equation is discussed for the case of position-dependent mass. In particular, we have found that for highly excited states the mutual ordering of the inverse mass and momentum operator in the non-relativistic theory is not important.
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"abstract": "Exact solution of Dirac equation for a particle whose potential energy and\nmass are inversely proportional to the distance from the force centre has been\nfound. The bound states exist provided the length scale $a$ which appears in\nthe expression for the mass is smaller than the classical electron radius\n$e^2/mc^2$. Furthermore, bound states also exist for negative values of $a$\neven in the absence of the Coulomb interaction. Quasirelativistic expansion of\nthe energy has been carried out, and a modified expression for the fine\nstructure of energy levels has been obtained. The problem of kinetic energy\noperator in the Schr\\\"odinger equation is discussed for the case of\nposition-dependent mass. In particular, we have found that for highly excited\nstates the mutual ordering of the inverse mass and momentum operator in the\nnon-relativistic theory is not important.",
"arxiv_id": "quant-ph/0502105",
"authors": [
"I. O. Vakarchuk"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/38/21/016",
"title": "Kepler problem in Dirac theory for a particle with position-dependent mass",
"url": "https://arxiv.org/abs/quant-ph/0502105"
},
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