Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 2 (2006), 062, 12 pages      quant-ph/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 Hamilton-Jacobi 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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