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The realizations of the Lie algebra corresponding to the dynamical symmetrygroup SO(2,1) of the Kepler and oscillator potentials are q-deformed. Theq-canonical transformation connecting two realizations is given and a generaldefinition for q-canonical transformation is deduced. q-Schr\"{o}dingerequation for a Kepler like potential is obtained from the q-oscillatorSchr\"{o}dinger equation. Energy spectrum and the ground state wave functionare calculated.Comment: 12 pages, Latex twice, (Comparison with the other approaches and some  refs. added. The version which will appear in J. Phys. A

slq(2) realizations for Kepler and oscillator potentials and q-canonical transformations

sl_q(2) realizations for Kepler and oscillator potentials and q-canonical transformations