On a q-analogue of the spin-orbit coupling

Based on the tensor method, a q-analogue of the spin-orbit coupling is intr oduced in a q-deformed Schrodinger equation, previously derived for a centr al potential. Analytic expressions for the matrix elements of the represent ations j = l +/- 1/2 are derived. The spectra of the harmonic oscillator an d the Coulomb potential are calculated numerically as a function of the def ormation parameter, without and with the spin-orbit coupling. The harmonic oscillator spectrum presents strong analogies with the bound spectrum of a Woods-Saxon potential customarily used in nuclear physics. The Coulomb spec trum simulates relativistic effects. The addition of the spin-orbit couplin g reinforces this picture.