The Hellmann-Feynman theorem and the spectrum of some Hamiltonian operators

TL;DR

This paper uses the Hellmann-Feynman theorem to demonstrate that certain non-relativistic Hamiltonian operators have an infinite spectrum of bound states.

Contribution

It provides a novel proof leveraging the Hellmann-Feynman theorem to establish the existence of infinitely many bound states for specific Hamiltonians.

Findings

Non-relativistic Hamiltonians support infinite bound states

Application of Hellmann-Feynman theorem to spectral analysis

Proof technique for spectral properties of Hamiltonians

Abstract

In this short note we resort to the well known Hellmann-Feynman theorem to prove that some non-relativistic Hamiltonian operators support an infinite number of bound states.