The behavior of the quantum potential is studied for a particle in a linear
and a harmonic potential by means of an extended phase space technique. This is
done by obtaining an expression for the quantum potential in momentum space
representation followed by the generalization of this concept to extended phase
space. It is shown that there exists an extended canonical transformation that
removes the expression for the quantum potential in the dynamical equation. The
situation, mathematically, is similar to disappearance of the centrifugal
potential in going from the spherical to the Cartesian coordinates that changes
the physical potential to an effective one. The representation where the
quantum potential disappears and the modified Hamilton-Jacobi equation reduces
to the familiar classical form, is one in which the dynamical equation turns
out to be the Wigner equation.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA