Abstract
Spectra of the operatorXp=qpN(a++a)qpN,p∈R, for theq-deformed oscillator algebra are studied. This operator tends to the position operator of the usual quantum harmonic oscillator ifq → 1. These spectra depend on the values ofq andp. The operatorXp can be bounded or unbounded. In the unbounded case, it is not selfadjoint and has infinitely many selfadjoint extensions.
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