Symmetry Transformation in Extended Phase Space: the Harmonic Oscillator in the Husimi Representation

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dc.creatorBahrami, Samira
dc.creatorNasiri, Sadolah
dc.date2008-02-04
dc.date.accessioned2026-07-07T09:34:51Z
dc.date.available2026-07-07T09:34:51Z
dc.descriptionIn a previous work the concept of quantum potential is generalized into extended phase space (EPS) for a particle in linear and harmonic potentials. It was shown there that in contrast to the Schrödinger quantum mechanics by an appropriate extended canonical transformation one can obtain the Wigner representation of phase space quantum mechanics in which the quantum potential is removed from dynamical equation. In other words, one still has the form invariance of the ordinary Hamilton-Jacobi equation in this representation. The situation, mathematically, is similar to the disappearance of the centrifugal potential in going from the spherical to the Cartesian coordinates. Here we show that the Husimi representation is another possible representation where the quantum potential for the harmonic potential disappears and the modified Hamilton-Jacobi equation reduces to the familiar classical form. This happens when the parameter in the Husimi transformation assumes a specific value corresponding to $Q$-function.
dc.descriptionThis is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
dc.identifierhttps://arxiv.org/abs/0802.0482
dc.identifierhttp://arxiv.org/abs/0802.0482
dc.identifierSIGMA 4 (2008), 014, 7 pages
dc.identifierdoi:10.3842/SIGMA.2008.014
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159644
dc.subjectQuantum Physics
dc.titleSymmetry Transformation in Extended Phase Space: the Harmonic Oscillator in the Husimi Representation
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