Boundary contributions to the hypervirial theorem

TL;DR

This paper investigates how boundary conditions can modify the virial theorem, analyzing the origin of additional boundary terms and computing them for specific quantum systems like Coulomb and harmonic oscillators.

Contribution

It introduces a generalized form of the virial theorem accounting for boundary contributions and demonstrates this with explicit examples.

Findings

Boundary conditions can lead to extra terms in the virial theorem.

Explicit calculations for Coulomb and harmonic oscillator systems show the boundary contributions.

The generalized theorem provides a more complete understanding of quantum systems with boundary effects.

Abstract

It is shown that under certain boundary conditions the virial theorem has to be modified. We analyze the origin of the extra term and compute it in particular examples. The Coulomb and harmonic oscillator with point interaction have been studied in the light of this generalization of the virial theorem.