Generalization of Hypervirial and Feynman-Hellmann Theorems for Singular Potentials

TL;DR

This paper extends the hypervirial and Feynman-Hellmann theorems to singular potentials in quantum mechanics, covering Schrödinger and Klein-Gordon equations, and discusses their physical implications and differences.

Contribution

It generalizes the hypervirial and Feynman-Hellmann theorems to singular potentials for a broad class of second order differential equations in quantum physics.

Findings

Extended theorems to singular potentials in Schrödinger and Klein-Gordon equations

Analyzed physical consequences of the generalized theorems

Highlighted differences between hypervirial and Feynman-Hellmann approaches

Abstract

Using well-known methods we generalize (hyper)virial theorems to case of singular potential. Discussion is performed for most general second order differential equation, which involves all physically interesting cases, as Schrodinger and Klein-Gordon equations with singular potentials. Some physical consequences are discussed. The connection with Feynman-Hellmann like theorems are also considered and some relevant differences are underlined.