Spectra of observables in the q-oscillator and q-analogue of the Fourier transform
Klimyk, Anatoliy
arXiv, 0508032 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2005-08-15
Classification:  Mathematical Physics,  Mathematics - Spectral Theory,  81Q10,  81S05,  41B15 
@article{0508032,
     author = {Klimyk, Anatoliy},
     title = {Spectra of observables in the q-oscillator and q-analogue of the Fourier
  transform},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0508032}
}

Klimyk, Anatoliy. Spectra of observables in the q-oscillator and q-analogue of the Fourier
  transform. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0508032/