2025-02-23T13:54:17-05:00 DEBUG: VuFindSearch\Backend\Solr\Connector: Query fl=%2A&wt=json&json.nl=arrarr&q=id%3A%22irk-123456789-148417%22&qt=morelikethis&rows=5
2025-02-23T13:54:17-05:00 DEBUG: VuFindSearch\Backend\Solr\Connector: => GET http://localhost:8983/solr/biblio/select?fl=%2A&wt=json&json.nl=arrarr&q=id%3A%22irk-123456789-148417%22&qt=morelikethis&rows=5
2025-02-23T13:54:17-05:00 DEBUG: VuFindSearch\Backend\Solr\Connector: <= 200 OK
2025-02-23T13:54:17-05:00 DEBUG: Deserialized SOLR response
Deformed su(1,1) Algebra as a Model for Quantum Oscillators
The Lie algebra su(1,1) can be deformed by a reflection operator, in such a way that the positive discrete series representations of su(1,1) can be extended to representations of this deformed algebra su(1,1)γ. Just as the positive discrete series representations of su(1,1) can be used to model a qu...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2012
|
| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/148417 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| id |
irk-123456789-148417 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1484172019-02-19T01:31:03Z Deformed su(1,1) Algebra as a Model for Quantum Oscillators Jafarov, E.I. Stoilova, N.I. Van der Jeugt, J. The Lie algebra su(1,1) can be deformed by a reflection operator, in such a way that the positive discrete series representations of su(1,1) can be extended to representations of this deformed algebra su(1,1)γ. Just as the positive discrete series representations of su(1,1) can be used to model a quantum oscillator with Meixner-Pollaczek polynomials as wave functions, the corresponding representations of su(1,1)γ can be utilized to construct models of a quantum oscillator. In this case, the wave functions are expressed in terms of continuous dual Hahn polynomials. We study some properties of these wave functions, and illustrate some features in plots. We also discuss some interesting limits and special cases of the obtained oscillator models. 2012 Article Deformed su(1,1) Algebra as a Model for Quantum Oscillators / E.I. Jafarov, N.I. Stoilova, J. Van der Jeugt // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 33 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81R05; 81Q65; 33C45 DOI: http://dx.doi.org/10.3842/SIGMA.2012.025 http://dspace.nbuv.gov.ua/handle/123456789/148417 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
The Lie algebra su(1,1) can be deformed by a reflection operator, in such a way that the positive discrete series representations of su(1,1) can be extended to representations of this deformed algebra su(1,1)γ. Just as the positive discrete series representations of su(1,1) can be used to model a quantum oscillator with Meixner-Pollaczek polynomials as wave functions, the corresponding representations of su(1,1)γ can be utilized to construct models of a quantum oscillator. In this case, the wave functions are expressed in terms of continuous dual Hahn polynomials. We study some properties of these wave functions, and illustrate some features in plots. We also discuss some interesting limits and special cases of the obtained oscillator models. |
| format |
Article |
| author |
Jafarov, E.I. Stoilova, N.I. Van der Jeugt, J. |
| spellingShingle |
Jafarov, E.I. Stoilova, N.I. Van der Jeugt, J. Deformed su(1,1) Algebra as a Model for Quantum Oscillators Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Jafarov, E.I. Stoilova, N.I. Van der Jeugt, J. |
| author_sort |
Jafarov, E.I. |
| title |
Deformed su(1,1) Algebra as a Model for Quantum Oscillators |
| title_short |
Deformed su(1,1) Algebra as a Model for Quantum Oscillators |
| title_full |
Deformed su(1,1) Algebra as a Model for Quantum Oscillators |
| title_fullStr |
Deformed su(1,1) Algebra as a Model for Quantum Oscillators |
| title_full_unstemmed |
Deformed su(1,1) Algebra as a Model for Quantum Oscillators |
| title_sort |
deformed su(1,1) algebra as a model for quantum oscillators |
| publisher |
Інститут математики НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148417 |
| citation_txt |
Deformed su(1,1) Algebra as a Model for Quantum Oscillators / E.I. Jafarov, N.I. Stoilova, J. Van der Jeugt // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 33 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT jafarovei deformedsu11algebraasamodelforquantumoscillators AT stoilovani deformedsu11algebraasamodelforquantumoscillators AT vanderjeugtj deformedsu11algebraasamodelforquantumoscillators |
| first_indexed |
2023-05-20T17:30:39Z |
| last_indexed |
2023-05-20T17:30:39Z |
| _version_ |
1796153455510814720 |