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

TL;DR

This paper investigates the impact of additional surface terms in hypervirial and Ehrenfest theorems for spherically symmetric potentials, emphasizing their importance for accurate physical predictions and deriving new results.

Contribution

It introduces the role of boundary terms in hypervirial and Ehrenfest theorems for spherical potentials and demonstrates their significance through various model potentials, including new findings.

Findings

Extra boundary terms are crucial for correct physical results.

Inclusion of these terms affects regular and singular potentials.

New analytical results are derived for specific potentials.

Abstract

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.