| Autor: |
Anatoliy U. Klimyk |
| Jazyk: |
angličtina |
| Rok vydání: |
2005 |
| Předmět: |
|
| Zdroj: |
Symmetry, Integrability and Geometry: Methods and Applications, Vol 1, p 008 (2005) |
| Druh dokumentu: |
article |
| ISSN: |
1815-0659 |
| Popis: |
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. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
|
