On the Wigner-Kirkwood Expansion of the Free Energy and the Evaluation of the Quantum Correction

Atoms

卷:10

François Soubiran¹  Jean-Christophe Pain¹  Luc Kazandjian¹ 

[1] CEA, DAM, DIF, F-91297 Arpajon, France;

关键词: partition function;    canonical ensemble;    Wigner-Kirkwood quantum correction;    classical limit;    one-component plasma;   

DOI  :  10.3390/atoms10020065

来源: DOAJ

【 摘 要 】

The Wigner-Kirkwood expansion of the quantum correction to the classical free energy is generally said to be in powers of ${\hslash }^2$ 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 ${\lambda }^2/a^2$, where $\lambda$ 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.

【 授权许可】

Unknown