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Spectra of observables in the q-oscillator and q-analogue of the Fourier transform
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.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA
Folksonomies vs. Bag-of-Words: The Evaluation & Comparison of Different Types of Document Representations
published or submitted for publicationis peer reviewe
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