Mathematics – Quantum Algebra
Scientific paper
1999-07-20
Mathematics
Quantum Algebra
6 pages latex, presented at the 8th Colloquium "Quantum groups and Integrable systems", Prague 17-19 June 1999
Scientific paper
10.1023/A:1022829132541
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.
Irac-Astaud Michele
Quesne Christiane
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