Generalization of the Hellmann-Feynman theorem

TL;DR

This paper extends the Hellmann-Feynman theorem to cases where the Hamiltonian's domain varies with a parameter, broadening its applicability in quantum mechanics.

Contribution

It introduces a generalized form of the Hellmann-Feynman theorem that accounts for parameter-dependent domains of the Hamiltonian.

Findings

The theorem now applies to Hamiltonians with parameter-dependent domains.

Provides a mathematical framework for the generalized theorem.

Enhances the theoretical tools for quantum systems analysis.

Abstract

The well known Hellmann-Feynman theorem of Quantum Mechanics connected with the derivative of the eigenvalues with respect to a parameter upon which the Hamiltonian depends, is generalized to include cases in which the domain of definition of the Hamiltonian of the system also depends on that parameter.