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Advances in Physical Chemistry
Volume 2014, Article ID 912054, 9 pages
http://dx.doi.org/10.1155/2014/912054
Research Article

Evaluation of Density Matrix and Helmholtz Free Energy for Harmonic Oscillator Asymmetric Potential via Feynmans Approach

1Chemistry Division, Faculty of Science and Technology, Phetchabun Rajabhat University, Phetchabun 67000, Thailand
2Physics Division, Faculty of Science and Technology, Phetchabun Rajabhat University, Phetchabun 67000, Thailand

Received 18 August 2014; Revised 8 October 2014; Accepted 9 October 2014; Published 2 November 2014

Academic Editor: Miquel Solà

Copyright © 2014 Piyarut Moonsri and Artit Hutem. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We apply a Feynmans technique for calculation of a canonical density matrix of a single particle under harmonic oscillator asymmetric potential and solving the Bloch equation of the statistical mechanics system. The density matrix and kinetic energy per unit length can be directly evaluated from the solving solutions. From the evaluation, it was found that both of the density matrix and kinetic energy per unit length depended on the parameter of the value of asymmetric potential , the value of axes-shift potential , and temperature (T). Comparison of the Helmholtz free energy was derived by the Feynmans technique and the path-integral method. The results illustrated are slightly different.