
SIGMA 2 (2006), 062, 12 pages quantph/0511125
https://doi.org/10.3842/SIGMA.2006.062
Quantum Potential and Symmetries in Extended Phase Space
Sadollah Nasiri ^{a, b}
^{a)} Department of Physics, Zanjan University, Zanjan, Iran
^{b)} Institute for Advanced Studies in Basic Sciences, IASBS, Zanjan, Iran
Received January 06, 2006, in final form May 19, 2006; Published online June 27, 2006
Abstract
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 HamiltonJacobi equation reduces to the familiar
classical form, is one in which the dynamical equation turns out
to be the Wigner equation.
Key words:
quantum potential; Wigner equation; distribution functions; extended phase space.
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