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

Arik M; Barut A O; Biedenharn L C; Bonatsos D; Burban I M; Carow-Watamura U; Dayi Ö F; Drienfeld V; Duru I H; Duru I H; Faddeev L; Filippov A T; Gangopadhyay D; I H Duru; Jimbo M; Macfarlane A J; Minahan J A; O F Dayi; Shabanov S V; Song X C; Vilenkin N; Woronowicz S; Yu Manin; Zumino B

research

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

Authors: Arik M
Barut A O
Biedenharn L C
Bonatsos D
Burban I M
Carow-Watamura U
Dayi Ö F
Drienfeld V
Duru I H
Duru I H
Faddeev L
Filippov A T
Gangopadhyay D
I H Duru
Jimbo M
Macfarlane A J
Minahan J A
O F Dayi
Shabanov S V
Song X C
Vilenkin N
Woronowicz S
Yu Manin
Zumino B
Publication date: 1 January 1995
Publisher: 'IOP Publishing'
Doi

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