Application of Modified Hypervirial and Ehrenfest Theorems and Some of its Consequences

It is well-known that owing to the restricted character of the area additional surface terms emerge in the traditional form of hypervirial and/or Ehrenfest theorems. Especially, when one considers spherically symmetric potentials and operators the radial distance in spherical coordinates is restricted by a half-plane. Therefore the extra term arises in this case as well in view of boundary conditions at the origin of coordinates. We analyse the role of this term for various model-potentials in the Schrodinger equation. We consider regular as well as soft-singular potentials and show that the inclusion of this extra term is very essential in obtaining correct physical results. Among the well-known results some new ones are also derived.