Speaker
Description
Elaboration of some fundamental relations in 3-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’s time derivative and the time derivative of the 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.
