Differential representations of dynamical oscillator symmetries in discrete Hilbert space
As a very important example for dynamical symmetries in the context of q-generalized quantum mechanics the algebra aa†−q−2a†a=1 is investigated. It represents the oscillator symmetry SUq(1,1) and is regarded as a commutation phenomenon of the q-Heisenberg algebra which provides a discrete spectrum o...
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| Format: | Article |
| Language: | English |
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Wiley
2000-01-01
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| Series: | Discrete Dynamics in Nature and Society |
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| Online Access: | http://dx.doi.org/10.1155/S1026022600000455 |
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| _version_ | 1832548134599786496 |
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| author | Andreas Ruffing |
| author_facet | Andreas Ruffing |
| author_sort | Andreas Ruffing |
| collection | DOAJ |
| description | As a very important example for dynamical symmetries in the context of q-generalized quantum mechanics the algebra aa†−q−2a†a=1 is investigated. It represents the oscillator symmetry SUq(1,1) and is regarded as a commutation phenomenon of the q-Heisenberg algebra which provides a discrete spectrum of momentum and space, i.e., a discrete Hilbert space structure. Generalized q-Hermite functions and systems of creation and annihilation operators are derived. The classical limit q→1 is investigated. Finally the SUq(1,1) algebra is represented by the dynamical variables of the q-Heisenberg algebra. |
| format | Article |
| id | doaj-art-9c54aedee6aa43d69f26fc7980753a30 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2000-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-9c54aedee6aa43d69f26fc7980753a302025-02-03T06:42:06ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2000-01-01529710610.1155/S1026022600000455Differential representations of dynamical oscillator symmetries in discrete Hilbert spaceAndreas Ruffing0Zentrum Mathematik, Technische Universität München, Arcisstrasse, 21/H4, München D-80333, GermanyAs a very important example for dynamical symmetries in the context of q-generalized quantum mechanics the algebra aa†−q−2a†a=1 is investigated. It represents the oscillator symmetry SUq(1,1) and is regarded as a commutation phenomenon of the q-Heisenberg algebra which provides a discrete spectrum of momentum and space, i.e., a discrete Hilbert space structure. Generalized q-Hermite functions and systems of creation and annihilation operators are derived. The classical limit q→1 is investigated. Finally the SUq(1,1) algebra is represented by the dynamical variables of the q-Heisenberg algebra.http://dx.doi.org/10.1155/S1026022600000455Quantum mechanics; Harmonic q-oscillators. |
| spellingShingle | Andreas Ruffing Differential representations of dynamical oscillator symmetries in discrete Hilbert space Discrete Dynamics in Nature and Society Quantum mechanics; Harmonic q-oscillators. |
| title | Differential representations of dynamical oscillator symmetries in discrete Hilbert space |
| title_full | Differential representations of dynamical oscillator symmetries in discrete Hilbert space |
| title_fullStr | Differential representations of dynamical oscillator symmetries in discrete Hilbert space |
| title_full_unstemmed | Differential representations of dynamical oscillator symmetries in discrete Hilbert space |
| title_short | Differential representations of dynamical oscillator symmetries in discrete Hilbert space |
| title_sort | differential representations of dynamical oscillator symmetries in discrete hilbert space |
| topic | Quantum mechanics; Harmonic q-oscillators. |
| url | http://dx.doi.org/10.1155/S1026022600000455 |
| work_keys_str_mv | AT andreasruffing differentialrepresentationsofdynamicaloscillatorsymmetriesindiscretehilbertspace |