DISTRIBUTION FUNCTIONS IN LIGHT OF THE UNCERTAINTY PRINCIPLE

Document Type: Regular Paper

Author

Department of Physics, Zanjan University, Zanjan, I. R. of Iran and Institute for Advanced Studies in Basic Sciences, IASBS, Zanjan, I. R. of Iran

Abstract

Here, we have considered the Husimi and Wigner distribution functions. We have, in
particular, shown how the uncertainty principle works for the two cases of simple and damped harmonic
oscillators when either of these two distributions are used. The conclusion shows that the Husimi
distribution function remains non-negative through the phase space but it does not always satisfies the
uncertainty principle. On the other hand the Wigner distribution function while becoming negative in
certain regions of the phase space do not violate the uncertainty principle.

Keywords