Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1909.10298 · American Journal of Physics

The Hellmann–Feynman theorem at finite temperature

Marina Pons, Bruno Juliá-Díaz, Artur Polls, Arnau Rios, Isaac Vidaña

Published May 21, 2020• 13 citations
arXivHTMLPDF

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 no direct access to the thermal average of the operators themselves.

DOI
10.1119/10.0001233

Related papers

Generalisation of the Hellmann-Feynman theorem to Gamow states

P. Ziesche, Karsten Kunze, B. Milek

The Hellmann-Feynman theorem valid for the parameter dependence of bound states is generalised to the case of Gamow states using an appropriate definition of scalar products and expectation values with such states. The one-dimensional square well potential is considered as an illustrative example.

Journal of Physics A Mathematical and General•Jul 11, 1987•12 citations

Deriving Internal Energy by Virtue of Generalized Feynman–Hellmann Theorem for Mixed States

Hong-Yi Fan, Zhonghua Jiang

We show how to directly use the generalized Feynman–Hellmann theorem, which is suitable for mixed state ensemble average, to derive the internal energy of Hamiltonian systems. A concrete example, which is a two coupled harminic oscillators, is used for elucidating our approach.

Communications in Theoretical Physics•Dec 1, 2005•1 citation

On the Hellmann-Feynman theorem for statistical averages

Francisco Marcelo Fernández

We discuss the Hellmann-Feynman theorem for degenerate states and its application to the calculation of the derivatives of statistical averages with respect to external parameters.

arXiv:1211.5958•Nov 26, 2012•0 citations

Deriving Internal Energy by Virtue of Generalized Feynman-Hellmann Theorem for Mixed States

Fan Fan, Hong-Yi, Jiang +1 more

We show how to directly use the generalized Feynman-Hellmann theorem, which is suitable for mixed state ensemble average, to derive the internal energy of Hamiltonian systems. A concrete example, which is a two coupled harminic oscillators, is used for elucidating our approach.

理论物理通讯：英文版•Jan 1, 2005•0 citations

An elementary derivation of the quantum virial theorem from Hellmann–Feynman theorem

Y. İpekoğlu, S. Turgut

Abstract A simple proof of the quantum virial theorem that can be used in undergraduate courses is given. The proof proceeds by first showing that the energy eigenvalues of a Hamiltonian remain invariant under a scale transformation. Then invoking the Hellmann–Feynman theorem produces the final statement of the virial theorem.

European Journal of Physics•Jun 1, 2016•6 citations

Mean energy of some interacting bosonic systems derived by virtue of the generalized Hellmann–Feynman theorem

Hong-Yi Fan, Xue-xiang Xu

By virtue of the generalized Hellmann–Feynman theorem [H. Y. Fan and B. Z. Chen, Phys. Lett. A 203, 95 (1995)], we derive the mean energy of some interacting bosonic systems for some Hamiltonian models without proceeding with diagonalizing the Hamiltonians. Our work extends the field of applications of the Hellmann–Feynman theorem and may enrich the theory of quantum statistics.

Journal of Mathematical Physics•Jun 1, 2009•7 citations
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.