  It is shown that in a quantized space determined by the $B_2\quad
(O(5)=Sp(4))$ algebra with three dimensional parameters of the length $L^2$,
momentum $(Mc)^2$, and action $S$, the spectrum of the Coulomb problem with
conserving Runge-Lenz vector coincides with the spectrum found by Schr\"odinger
for the space of constant curvature but with the values of the principal
quantum number limited from the side of higher values. The same problem is
solved for the spectrum of a harmonic oscillator.
