  Elaboration of some fundamental relations in three dimensional quantum
mechanics is considered taking into account the restricted character of areas
in radial distance. In such cases the boundary behavior of the radial wave
function and singularity of operators at the origin of coordinates contribute
to these relations. We derive the relation between the average value of the
operator time derivative and the time derivative of mean value of this
operator, which is usually considered to be the same by definition. The
deviation from the known result is deduced and manifested by extra term, which
depends on the boundary behavior mentioned above. The general form for this
extra term takes place in the hypervirial like theorems. As a particular case,
the virial theorem for Coulomb and oscillator potentials is considered and
correction to the Kramers sum rule is derived. Moreover the corrected Ehrenfest
theorem is deduced and its consistency with real physical picture is
demonstrated.
