Extended Wigner function for the harmonic oscillator in the phase space

• Published in: Results in physics Vol. 19; p. 103546
• Main Authors: Perepelkin, E.E., Sadovnikov, B.I., Inozemtseva, N.G., Burlakov, E.V.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.12.2020; Elsevier
• Subjects: Exact solution; Harmonic oscillator; Moyal equation; Rigorous result; Wave equation; Wigner function; Wave equation; Wigner function; Moyal equation; Rigorous result; Harmonic oscillator; Exact solution
• ISSN: 2211-3797; 2211-3797
• DOI: 10.1016/j.rinp.2020.103546

•Interpretation of the negative probability.•Exact solution of the Moyal equation.•Time depended quasi-probability function for quantum harmonic oscillator. New time dependent extended Wigner functions for the quantum harmonic oscillator have been obtained in this work. The Moyal equation for the harmonic oscillator has been associated with the wave equation of a 2D membrane in the phase plane. The values of the extended 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 extended Wigner function correspond to the direction of the deviation from the equilibrium state. As an example, a time dependent extended Wigner function corresponding to the standing wave of quasi-probability density arising in the phase plane is considered.