Spectra of Observables in the q-Oscillator and q-Analogue of the Fourier Transform

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2005
• Main Author: Klimyk, A.U.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2005
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/209352
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Spectra of Observables in the q-Oscillator and q-Analogue of the Fourier Transform / A.U. Klimyk // Symmetry, Integrability and Geometry: Methods and Applications. — 2005. — Т. 1. — Бібліогр.: 22 назв. — англ.

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 ex...