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The Hellmann–Feynman theorem at finite temperature

Pons, Marina, Juliá-Díaz, Bruno, Polls, Artur, Rios, Arnau and Vidaña, Isaac (2020) The Hellmann–Feynman theorem at finite temperature American Journal of Physics, 88 (6). pp. 503-510.

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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.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Physics
Authors :
Pons, Marina
Juliá-Díaz, Bruno
Polls, Artur
Vidaña, Isaac
Date : 21 May 2020
Funders : Science and Technology Facilities Council (STFC)
DOI : 10.1119/10.0001233
Copyright Disclaimer : © 2020 American Association of Physics Teachers. for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in American Journal of Physics 88;6, pp.503-510 and may be found at
Depositing User : Clive Harris
Date Deposited : 01 Jun 2020 11:24
Last Modified : 01 Jun 2020 11:24

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