  We found hermitian realizations of the position vector $\vec{r}$, the angular
momentum $\vec{\Lambda}$ and the linear momentum $\vec{p}$, all behaving like
vectors under the $su_q(2)$ algebra, generated by $L_0$ and $L_\pm$. They are
used to introduce a $q$-deformed Schr\" odinger equation. Its solutions for the
particular cases of the Coulomb and the harmonic oscillator potentials are
given and briefly discussed.
