Wigner Function for Harmonic Oscillator and The Classical Limit

The Wigner function is a quantum analogue of the classical joined distribution of position and momentum. As such is should be a good tool to study quantum-classical correspondence. In this paper, the classical limit of the Wigner function is shown using the quantum harmonic oscillator as an example....

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Bibliographic Details
Published inarXiv.org
Main Authors Mostowski, Jan, Pietraszewicz, Joanna
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 14.04.2021
Subjects
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Harmonic oscillators
Wave functions
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Summary:The Wigner function is a quantum analogue of the classical joined distribution of position and momentum. As such is should be a good tool to study quantum-classical correspondence. In this paper, the classical limit of the Wigner function is shown using the quantum harmonic oscillator as an example. The Wigner function is found exactly for all states. The semi-classical wavefunctions for highly excited states are used as the approach to the classical limit. Therefore, one can found the classical limit of the Wigner function for highly excited states and shown that it gives the classical microcanonical ensemble.
ISSN:2331-8422