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 |
| Published: |
Wiley
2000-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S1026022600000455 |
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| Summary: | 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. |
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| ISSN: | 1026-0226 1607-887X |