Nonstandard Deformed Oscillators from q- and p,q-Deformations of Heisenberg Algebra

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2016
• Hauptverfasser: Gavrilik, A.M., Kachurik, I.I.
• Format: Artikel
• Sprache: English
• Veröffentlicht: Інститут математики НАН України 2016
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/147738
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: 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.

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.