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.