Three theorems of quantum mechanics and their classical counterparts

TL;DR

This paper explores the connections between quantum and classical mechanics by extending three fundamental theorems to classical systems with nonstandard kinetic energy, revealing insights into their relationship.

Contribution

It demonstrates that the Hellmann-Feynman, virial, and comparison theorems hold for classical mechanics with nonstandard kinetic energy, expanding their applicability.

Findings

The three theorems are valid for classical mechanics with nonstandard kinetic energy.

Provides constraints on the functional form of kinetic energy in classical systems.

Enhances understanding of quantum-classical correspondence.

Abstract

The Hellmann-Feynman, virial and comparison theorems are three fundamental theorems of quantum mechanics. For the first two, counterparts exist for classical mechanics with relativistic or nonrelativistic kinetic energy. It is shown here that these three theorems are valid for classical mechanics with a nonstandard kinetic energy. This brings some information about the connections between the quantum and classical worlds. Constraints about the functional form of the kinetic energy are also discussed.