Mathematics – Quantum Algebra
Scientific paper
1998-03-22
Mathematics
Quantum Algebra
32 pages, LaTeX2e, amssymb,latexsym,amsfonts, no figures
Scientific paper
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.
Borzov Vadim V.
Damaskinsky Eugene V.
Kulish Petr P.
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