Symmetry transformation in extended phase space: the harmonic oscillator in the Husimi representation
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Publication:2473558
DOI10.3842/SIGMA.2008.014zbMATH Open1133.81043arXiv0802.0482MaRDI QIDQ2473558
Author name not available (Why is that?)
Publication date: 27 February 2008
Published in: (Search for Journal in Brave)
Abstract: In 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 Schr"odinger 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 -function.
Full work available at URL: https://arxiv.org/abs/0802.0482
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