**The effect of symmetry transformation on the quantum potential in extended phase space**

**Abstract:**

In the extended phase space approach to quantum mechanics, it is possible to obtain different distribution
functions by appropriate canonical transformations in classical level and corresponding unitary transformations in quantum
level[1,2]. It is shown that the quantum potential depends on the kind of distribution functions that one uses to solve the
problems [3]. This permits one to find a representation with a specified symmetry in the extended phase space for which the
quantum potential could be removed at all. As an example, the Wigner distribution function serves to remove the quantum
potential for a simple harmonic oscillator [3]. Here it is shown that a) the Husimi distribution function could be obtained
by an appropriate canonical transformation on Wigner function in extended phase space having a single arbitrary parameter.
b) the quantum potential could be removed from the dynamical equation of Husimi distribution function for a fix value of
the parameter involved. Thus, the Hamilton-Jacobi equation takes its standard format in the extended phase space by
excluding the quantum potential for Husimi distribution function.

[2]. S. Nasiri, Y. Sobouti and F. Taati, “Phase space quantum mechanics-direct” J. Math. Phys. 47, 092106, 2006.

[3]. S. Nasiri “Quantum potential and symmetries in extended phase space” SIGMA 2 (2006), Paper 062.

Joint work with *Sadollah Nasiri* (Zanjan University and Institute for Advanced Studies in Basic Sciences, Zanjan, Iran).