$sl_q(2)$ Realizations for Kepler and Oscillator Potentials and q-Canonical Transformations

Details $sl_q(2)$ Realizations for Kepler and Oscillator Potentials and q-Canonical Transformations $sl_q(2)$ Realizations for Kepler and Oscillator Potentials and q-Canonical Transformations

1994-10-25

arxiv.org/abs/hep-th/9410186v2

J.Phys. A28 (1995) 2395-2402

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1088/0305-4470/28/8/029

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-Schr\"{o}dinger equation for a Kepler like potential is obtained from the q-oscillator Schr\"{o}dinger equation. Energy spectrum and the ground state wave function are calculated.

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