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arXiv:hep-th/9908098

Partial algebraization and a q-deformed harmonic oscillator

Abilio De Freitas, S. Salamó

Published Aug 13, 1999• 0 citations
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Abstract

From the algebraic treatment of the quasi-solvable systems, and a q-deformation of the associated $su(2)$ algebra, we obtain exact solutions for the q-deformed Schrodinger equation with a 3-dimensional q-deformed harmonic oscillator potential.

DOI
10.48550/arxiv.hep-th/9908098

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From the algebraic treatment of the quasi-solvable systems, and a q-deformation of the associated su(2)su(2)su(2) algebra, we obtain exact solutions for the q-deformed Schrodinger equation with a 3-dimensional q-deformed harmonic oscillator potential.
We found hermitian realizations of the position vector r⃗\vec{r}r, angular momentum Λ⃗\vecΛΛ and linear momentum p⃗\vec{p}p​ behaving like vectors with respect to the SUq(2)SU_q(2)SUq​(2) algebra, generated by L0L_0L0​ and L±L_\pmL±​. They are used to write the qqq deformed Schrödinger equation, whose solution for Coulomb and oscillator potential are briefly discussed.
The possibility of q-deformation of known exactly solvable quantum mechanical models is considered via the dynamical symmetry of the radial problem. The algebraic structure of the D-dimensional simple harmonic oscillator is analysed from this point of view. In the two-dimensional case, q-deformed bosons are introduced for the radial degrees of freedom, which together with the standard angular operators yield the so(2)(+)so q (2,1) dynamical algebra. The corresponding Hilbert space is identified and possible q-deformed Hamiltonians described.