  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.
