On position operator spectral measure for deformed oscillator in the case of indetermine Hamburger moment problem

1998/03/22 by V. V. Borzov, Borzov, V. V., E. V. Damaskinsky +3 · 1 citation
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #math.QA

paper · pdf · doi:10.48550/arxiv.math/9803099

32 pages, LaTeX2e, amssymb,latexsym,amsfonts, no figures

arxiv created 1998/03/22 · arxiv updated 2009/11/30

Abstract

The spectral measure of the position (momentum) operator X for q-deformed oscillator is calculated in the case of the indetermine Hamburger moment problem. The exposition is given for concrete choice of generators for q-oscillator algebra, although developed technique apply for every other cases with indetermine moment problem. The Stieltjes transformation m(z) of spectral measure is expressed in terms of the entries of Jacobi matrix X only. The direct connection between values of parameters labeling the spectral measures and related selfadjoint extensions of X is established.

Cited by

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

Related

• Point mass perturbations of spectral measures
• Momentum and Position Representations for the q-deformed Euclidean Quantum Space
• q-deformed Fourier Theory
• Quadrature operator eigenstates and wavefunctions of f-deformed oscillators
• Phase operator problem and an index theorem for Q-deformed oscillator