Extended Wigner function for the harmonic oscillator in the phase space

2020/03/26 by E. E. Perepelkin, Perepelkin, E. E., Б. И. Садовников +5
Computer Science · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2003.11737

openalex publication_date 2020/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

New time dependent Wigner functions for the quantum harmonic oscillator have been obtained in this work. The Moyal equation for the harmonic oscillator has been presented as the wave equation of a 2D membrane in the phase plane. The values of the Wigner function are equal to the deviation values of the points on the surface of the membrane from the equilibrium state. The positive and negative values of the Wigner function correspond to the direction of the deviation from the equilibrium state. As an example, a time dependent Wigner function corresponding to the standing wave of quasi-probability density arising in the phase plane is considered.

Citations

• Distribution functions in physics: Fundamentals
• Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase
• Quantum mechanics as a statistical theory

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