dorsal/arxiv
View SchemaMatrix Hamiltonians: SUSY approach to hidden symmetries
| Authors | A. A. Andrianov, F. Cannata, D. N. Nishnianidze, M. V. Ioffe |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9707004 |
| URL | https://arxiv.org/abs/quant-ph/9707004 |
| DOI | 10.1088/0305-4470/30/14/015 |
| Journal | J.Phys.A30:5037-5050,1997 |
Abstract
A new supersymmetric approach to the analysis of dynamical symmetries for matrix quantum systems is presented. Contrary to standard one dimensional quantum mechanics where there is no role for an additional symmetry due to nondegeneracy, matrix hamiltonians allow for non-trivial residual symmetries. This approach is based on a generalization of the intertwining relations familiar in SUSY Quantum Mechanics. The corresponding matrix supercharges, of first or of second order in derivatives, lead to an algebra which incorporates an additional block diagonal differential matrix operator (referred to as a "hidden" symmetry operator) found to commute with the superhamiltonian. We discuss some physical interpretations of such dynamical systems in terms of spin 1/2 particle in a magnetic field or in terms of coupled channel problem. Particular attention is paid to the case of transparent matrix potentials.
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"abstract": "A new supersymmetric approach to the analysis of dynamical symmetries for\nmatrix quantum systems is presented. Contrary to standard one dimensional\nquantum mechanics where there is no role for an additional symmetry due to\nnondegeneracy, matrix hamiltonians allow for non-trivial residual symmetries.\nThis approach is based on a generalization of the intertwining relations\nfamiliar in SUSY Quantum Mechanics. The corresponding matrix supercharges, of\nfirst or of second order in derivatives, lead to an algebra which incorporates\nan additional block diagonal differential matrix operator (referred to as a\n\"hidden\" symmetry operator) found to commute with the superhamiltonian. We\ndiscuss some physical interpretations of such dynamical systems in terms of\nspin 1/2 particle in a magnetic field or in terms of coupled channel problem.\nParticular attention is paid to the case of transparent matrix potentials.",
"arxiv_id": "quant-ph/9707004",
"authors": [
"A. A. Andrianov",
"F. Cannata",
"D. N. Nishnianidze",
"M. V. Ioffe"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/30/14/015",
"journal_ref": "J.Phys.A30:5037-5050,1997",
"title": "Matrix Hamiltonians: SUSY approach to hidden symmetries",
"url": "https://arxiv.org/abs/quant-ph/9707004"
},
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