On the Hellmann-Feynman theorem for statistical averages

TL;DR

This paper explores the Hellmann-Feynman theorem's application to degenerate states and how it can be used to compute derivatives of statistical averages with respect to external parameters.

Contribution

It extends the Hellmann-Feynman theorem to degenerate states and applies it to statistical averages, providing a theoretical framework for such calculations.

Findings

Extended the theorem to degenerate states.

Derived formulas for derivatives of statistical averages.

Applicable to quantum systems with degeneracies.

Abstract

We discuss the Hellmann-Feynman theorem for degenerate states and its application to the calculation of the derivatives of statistical averages with respect to external parameters.