Table of Contents
Research Letters in Physics
Volume 2009 (2009), Article ID 298790, 5 pages
http://dx.doi.org/10.1155/2009/298790
Research Letter

Reality of the Wigner Functions and Quantization

1Department of Physics, Zanjan University, P. O. Box 45196-313, Zanjan 45371-38111, Iran
2Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), P. O. Box 45195-1159, Zanjan 45195-1159, Iran

Received 11 January 2009; Accepted 8 May 2009

Academic Editor: Nicholas Bigelow

Copyright © 2009 Sadollah Nasiri and Samira Bahrami. 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

Here we use the extended phase space formulation of quantum statistical mechanics proposed in an earlier work to define an extended lagrangian for Wigner's functions (WFs). The extended action defined by this lagrangian is a function of ordinary phase space variables. The reality condition of WFs is employed to quantize the extended action. The energy quantization is obtained as a direct consequence of the quantized action. The technique is applied to find the energy states of harmonic oscillator, particle in the box, and hydrogen atom as the illustrative examples.