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On the Heisenberg and orthosymplectic superalgebras of the harmonic oscillator. (English) Zbl 0649.17004
The n-dimensional quantum harmonic oscillator is discussed with respect to a new invariance superalgebra. The corresponding supersymmetric Hamiltonian is constructed and the superalgebra is compared with earlier results [the authors, J. Phys. A 21, 651-667 (1988) and M. J. Englefield, J. Phys. A 21, 1309-1319 (1988); see the preceding reviews Zbl 0649.17002 and Zbl 0649.17003)].
Reviewer: M.Baake

MSC:
17A70 Superalgebras
81S99 General quantum mechanics and problems of quantization
17B70 Graded Lie (super)algebras
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[1] DOI: 10.1016/0003-4916(83)90316-0 · doi:10.1016/0003-4916(83)90316-0
[2] DOI: 10.1016/0550-3213(81)90006-7 · Zbl 1258.81046 · doi:10.1016/0550-3213(81)90006-7
[3] DOI: 10.1088/0305-4470/21/3/020 · Zbl 0649.17002 · doi:10.1088/0305-4470/21/3/020
[4] Niederer U., Helv. Phys. Acta 46 pp 191– (1973)
[5] DOI: 10.1016/0550-3213(84)90422-X · doi:10.1016/0550-3213(84)90422-X
[6] DOI: 10.1103/PhysRevD.5.377 · doi:10.1103/PhysRevD.5.377
[7] DOI: 10.1103/PhysRevD.5.377 · doi:10.1103/PhysRevD.5.377
[8] DOI: 10.1088/0305-4470/21/6/008 · Zbl 0649.17003 · doi:10.1088/0305-4470/21/6/008
[9] DOI: 10.1063/1.526061 · Zbl 0563.17007 · doi:10.1063/1.526061
[10] DOI: 10.1016/0003-4916(85)90017-X · doi:10.1016/0003-4916(85)90017-X
[11] DOI: 10.1088/0305-4470/20/5/024 · Zbl 0634.35074 · doi:10.1088/0305-4470/20/5/024
[12] DOI: 10.1103/PhysRevD.32.2627 · doi:10.1103/PhysRevD.32.2627
[13] DOI: 10.1016/0370-2693(83)90134-X · doi:10.1016/0370-2693(83)90134-X
[14] DOI: 10.1016/0370-2693(85)90697-5 · doi:10.1016/0370-2693(85)90697-5
[15] DOI: 10.1016/0375-9601(86)90316-6 · doi:10.1016/0375-9601(86)90316-6
[16] Dehin D., Helv. Phys. Acta 60 pp 552– (1987)
[17] DOI: 10.1142/S0217751X88000187 · doi:10.1142/S0217751X88000187
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