  Based on the tensor method, a q-analoque of the spin-orbit coupling is
introduced in a q-deformed Schroedinger equation, previously derived for a
central potential. Analytic expressions for the matrix elemnets of the
representation j=l\pm 1/2 are derived. The spectra of the harmonic oscillator
and the Coulomb potential are calculated numerically as a function of the
deformation parameter, without and with the spin-orbit coupling. The harmonic
oscillator spectrum presents strong analogies with the bound spectrum of an
Woods-Saxon potential customarily used in nuclear physics. The Coulomb spectrum
simulates relativistic effects. The addition of the spin-orbit coupling
reinforces this picture.
