Spectra of observables in the q-oscillator and q-analogue of the Fourier transform
| dc.creator | Klimyk, Anatoliy | |
| dc.date | 2005-08-15 | |
| dc.date | 2005-11-25 | |
| dc.date.accessioned | 2026-07-07T09:34:21Z | |
| dc.date.available | 2026-07-07T09:34:21Z | |
| dc.description | Spectra of the position and momentum operators of the Biedenharn-Macfarlane q-oscillator (with the main relation aa^+-qa^+a=1) are studied when q>1. These operators are symmetric but not self-adjoint. They have a one-parameter family of self-adjoint extensions. These extensions are derived explicitly. Their spectra and eigenfunctions are given. Spectra of different extensions do not intersect. The results show that the creation and annihilation operators a^+ and a of the q-oscillator for q>1 cannot determine a physical system without further more precise definition. In order to determine a physical system we have to choose appropriate self-adjoint extensions of the position and momentum operators. | |
| dc.description | Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/ | |
| dc.identifier | https://arxiv.org/abs/math-ph/0508032 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0508032 | |
| dc.identifier | SIGMA 1 (2005), 008, 17 pages | |
| dc.identifier | doi:10.3842/SIGMA.2005.008 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159461 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Spectral Theory | |
| dc.subject | 81Q10; 81S05; 41B15 | |
| dc.title | Spectra of observables in the q-oscillator and q-analogue of the Fourier transform | |
| dc.type | text |