Nonstandard Deformed Oscillators from q- and p,q-Deformations of Heisenberg Algebra
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Nonstandard Deformed Oscillators from q- and p,q-Deformations of Heisenberg Algebra
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| Creator |
Gavrilik, A.M.
Kachurik, I.I. |
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| Description |
For the two-parameter p,q-deformed Heisenberg algebra introduced recently and in which, instead of usual commutator of X and P in the l.h.s. of basic relation [X,P]=iℏ, one uses the p,q-commutator, we established interesting properties. Most important is the realizability of the p,q-deformed Heisenberg algebra by means of the appropriate deformed oscillator algebra. Another uncovered property is special extension of the usual mutual Hermitian conjugation of the creation and annihilation operators, namely the so-called η(N)-pseudo-Hermitian conjugation rule, along with the related η(N)-pseudo-Hermiticity property of the position or momentum operators. In this work, we present some new solutions of the realization problem yielding new (nonstandard) deformed oscillators, and show their inequivalence to the earlier known solution and the respective deformed oscillator algebra, in particular what concerns ground state energy.
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| Date |
2019-02-15T18:57:44Z
2019-02-15T18:57:44Z 2016 |
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| Type |
Article
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| Identifier |
Nonstandard Deformed Oscillators from q- and p,q-Deformations of Heisenberg Algebra / A.M. Gavrilik, I.I. Kachurik // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 38 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 81R50; 81S05; 81Vxx; 17B37 DOI:10.3842/SIGMA.2016.047 http://dspace.nbuv.gov.ua/handle/123456789/147738 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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