Description
Title: Regarding the Evaluation of the Quantum Correction and the Wigner-Kirkwood Expansion of the Free Energy
Abstract: Only the first few terms of the Wigner-Kirkwood expansion of the quantum correction to the classical free energy are shown. This expansion is typically said to be in powers of h2. In this work, we obtain a general description of all terms in a dimensionless form using the Bloch differential equation. By an effective coupling constant, it is discovered that the first corrective term is proportional to the product of l2/a2, where l is the thermal de Broglie wavelength and a3 is the volume per particle. It is possible to gauge the quantum correction’s size using this dimensionless parameter. We demonstrate the significance of the magnitude of the potential on the quantum correction using the example of a one-component plasma. The emphasis is on a straightforward and didactic presentation even though the results presented are not inherently novel.
Keywords: partition function; canonical ensemble; Wigner-Kirkwood quantum correction; classical limit; one-component plasma
Paper Quality: SCOPUS / Web of Science Level Research Paper
Subject: Physics
Subject Category: Atomic and Molecular Physics, and Optics
Writer Experience: 20+ Years
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