$sl_q(2)$ Realizations for Kepler and Oscillator Potentials and   q-Canonical Transformations
  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. 
O.F. Dayi and I.H. Duru