Department of Physics, Zanjan University,

and

Institute for Advanced Studies in Basic Sciences, IASBS,

Zanjan, IRAN

E-mail: nasiri@iasbs.ac.ir

**Quantum Potential and Symmetries in Extended Phase
Space**

**Abstract:**

Here the concept of the quantum potential is looked upon the extended
phase space transformations. It seems that there exist a specific extended
canonical transformations for a any given potential that removes the quantum
potential from the dynamical equation. The point is something like the
suitable coordinate system chosen to convert the physical potential to
an effective one, such as the appearance of centrifugal potential in going
from Cartesian to spherical coordinates. As an Example the Wigner equation
is quantum potential-free equation for harmonic potential. This is obtained
by a suitable canonical transformation on Sobouti-Nasiri equation in extended
phase space keeping the Hamilton Jacobi equation form invariant.