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- Title
On the Wigner-Kirkwood Expansion of the Free Energy and the Evaluation of the Quantum Correction.
- Authors
Kazandjian, Luc; Soubiran, François; Pain, Jean-Christophe
- Abstract
The Wigner-Kirkwood expansion of the quantum correction to the classical free energy is generally said to be in powers of ℏ 2 and only its first few terms are presented. In this work, we use the Bloch differential equation to obtain a general description of all terms in a dimensionless form. The first corrective term turns out to be proportional to the product of λ 2 / a 2 , where λ is the thermal de Broglie wavelength and a 3 is the volume per particle, by an effective coupling constant. This dimensionless parameter can be used to assess the magnitude of the quantum correction. Using the one-component plasma as an illustration we highlight the importance of the magnitude of the potential on the quantum correction. The results presented are not formally new; the emphasis is placed on a simple and didactic presentation.
- Subjects
BLOCH equations; COUPLING constants; DIFFERENTIAL equations; PARTITION functions; CANONICAL ensemble
- Publication
Atoms (2218-2004), 2022, Vol 10, Issue 2, p65
- ISSN
2218-2004
- Publication type
Article
- DOI
10.3390/atoms10020065