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American Journal of Physics

Hellmann–Feynman theorem in a linear superposition of energy eigenstates

S. Balasubramanian

Published Dec 1, 1994• 4 citations
Publisher

Abstract

A generalization to the Hellmann–Feynman theorem is presented when the quantum mechanical state is a linear superposition of energy eigenstates. Some simple applications are discussed.
DOI
10.1119/1.17670

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We present a simple derivation of the Hellmann–Feynman theorem at finite temperature. We illustrate its validity by considering three relevant examples, which can be used in quantum mechanics lectures: the one-dimensional harmonic oscillator, the one-dimensional Ising model, and the Lipkin model. We show that the Hellmann–Feynman theorem allows one to calculate expectation values of operators that appear in the Hamiltonian. This is particularly useful when the total free energy is available, but there is no direct access to the thermal average of the operators themselves.