suq(2)-Invariant Harmonic Oscillator

Abstract

We propose a q-deformation of the su(2)-invariant Schrodinger equation of a spinless particle in a central potential, which allows us not only to determine a deformed spectrum and the corresponding eigenstates, as in other approaches, but also to calculate the expectation values of some physically-relevant operators. Here we consider the case of the isotropic harmonic oscillator and of the quadrupole operator governing its interaction with an external field. We obtain the spectrum and wave functions both for q in R+ and generic q in S1, and study the effects of the q-value range and of the arbitrariness in the suq(2) Casimir operator choice. We then show that the quadrupole operator in l=0 states provides a good measure of the deformation influence on the wave functions and on the Hilbert space spanned by them.