$s{l}_q(2)$ Realizations for Kepler and Oscillator Potentials and q-Canonical Transformations

Abstract

The realizations of the Lie algebra corresponding to the dynamical symmetry group SO(2,1) of the Kepler and oscillator potentials are q-deformed. The q-canonical transformation connecting two realizations is given and a general definition for q-canonical transformation is deduced. q-Schrödinger equation for a Kepler like potential is obtained from the q-oscillator Schrödinger equation. Energy spectrum and the ground state wave function are calculated.

12 pages, Latex twice, (Comparison with the other approaches and some refs. added. The version which will appear in J. Phys. A)

References in corpus (2)

• The $q$-deformed Schrödinger Equation of the Harmonic Oscillator on the Quantum Euclidian Space
• BFV--BRST Analysis of the Classical and Quantum q-deformations of the sl(2) Algebra

Cited by in corpus (3)

• Completeness of Coherent States Associated with Self-Similar Potentials and Ramanujan's Integral Extension of the Beta Function
• Green Function on the q-Symmetric Space SU_q(2)/U(1)
• q-deformed Star Products and Moyal Brackets