dorsal/arxiv
View SchemaGenerally relativistical Tetrode-Weyl-Fock-Ivanenko formalism and behaviour of quantum-mechanical particles of spin 1/2 in the Abelian monopole field
| Authors | V. M. Red'kov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9812002 |
| URL | https://arxiv.org/abs/quant-ph/9812002 |
Abstract
Some attention in the literature has been given to the case of a particle of spin 1/2 on the background of the external monopole potential. Some aspects of this problem are reexamined here. The primary technical novelty is that the tetrad generally relativistic method of Tetrode-Weyl-Fock-Ivanenko for describing a spinor particle is exploited. The choice of the formalism has turned out to be of great fruitfulness for examining the system. It is matter that, as known, the use of a special spherical tetrad in the theory of a spin 1/2 particle had led Schrodinger to a basis of remarkable features. The basis has been used with great efficiency by Pauli in his investigation on the pro- blem of allowed spherically symmetric wave functions in quantum mechanics. For our purposes, just several simple rules extracted from the much more com- prehensive Pauli's analysis will be quite sufficient; those are almost mnemo- nic working regulations. So, one may remember some very primary facts of D- functions theory and then produce automatically proper wave functions. It seems rather likely, that there may exist a generalized analog of such a re- presentation for J(i)-operators, that might be successfully used whenever in a linear problem there exists a spherical symmetry, irrespective of the con- crete embodiment of such a symmetry. In particular, the case of electron in the external Abelian monopole field completely come under the Sch-Pau method.
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"abstract": "Some attention in the literature has been given to the case of a particle of\nspin 1/2 on the background of the external monopole potential. Some aspects of\nthis problem are reexamined here. The primary technical novelty is that the\ntetrad generally relativistic method of Tetrode-Weyl-Fock-Ivanenko for\ndescribing a spinor particle is exploited. The choice of the formalism has\nturned out to be of great fruitfulness for examining the system. It is matter\nthat, as known, the use of a special spherical tetrad in the theory of a spin\n1/2 particle had led Schrodinger to a basis of remarkable features. The basis\nhas been used with great efficiency by Pauli in his investigation on the pro-\nblem of allowed spherically symmetric wave functions in quantum mechanics. For\nour purposes, just several simple rules extracted from the much more com-\nprehensive Pauli\u0027s analysis will be quite sufficient; those are almost mnemo-\nnic working regulations. So, one may remember some very primary facts of D-\nfunctions theory and then produce automatically proper wave functions. It seems\nrather likely, that there may exist a generalized analog of such a re-\npresentation for J(i)-operators, that might be successfully used whenever in a\nlinear problem there exists a spherical symmetry, irrespective of the con-\ncrete embodiment of such a symmetry. In particular, the case of electron in the\nexternal Abelian monopole field completely come under the Sch-Pau method.",
"arxiv_id": "quant-ph/9812002",
"authors": [
"V. M. Red\u0027kov"
],
"categories": [
"quant-ph"
],
"title": "Generally relativistical Tetrode-Weyl-Fock-Ivanenko formalism and behaviour of quantum-mechanical particles of spin 1/2 in the Abelian monopole field",
"url": "https://arxiv.org/abs/quant-ph/9812002"
},
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