The Hellmann-Feynman theorem at finite temperature
Quantum Physics
2020-06-24 v2 Quantum Gases
Statistical Mechanics
Nuclear Theory
Physics Education
Abstract
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 not direct access to the thermal average of the operators themselves.
Cite
@article{arxiv.1909.10298,
title = {The Hellmann-Feynman theorem at finite temperature},
author = {Marina Pons and Bruno Juliá-Díaz and Arnau Rios and Isaac Vidaña and Artur Polls},
journal= {arXiv preprint arXiv:1909.10298},
year = {2020}
}
Comments
8 pages, 3 figures. Updated version, accepted in American Journal of Physics