Generalised Virial theorems in Classical and Quantum Physics

TL;DR

This paper explores generalized virial theorems in classical and quantum physics, revealing new relations between matrix elements and extending the theorems to multiple dimensions.

Contribution

It provides a unified analysis of virial theorem generalizations in classical and quantum contexts, including matrix relations and multi-dimensional extensions.

Findings

Quantum virial theorem relates matrix elements.

Differences between classical and quantum generalizations identified.

Extensions to arbitrary dimensions discussed.

Abstract

Generalisations of the virial theorm in Classical Mechanics and Quantum Mechanics are examined. It is shown that the generalised virial theorem in Quantum Mechanics leads to certain relations between matrix elements. The differences between the generalisations in Classical and Quantum Mechanics are identified. Some results arising from the radial Schr\"odinger equation in Quantum Mechanics are discussed. It is also shown that the generalisations of the virial theorem may be extended to arbitrary number of dimensions.