Extended Wigner function for the harmonic oscillator in the phase space

Results in Physics

E.V. Burlakov¹  N.G. Inozemtseva²  B.I. Sadovnikov³  E.E. Perepelkin⁴ 

[1] Corresponding author at: Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia.;Dubna State University, Moscow Region, Moscow 141980, Russia;Moscow Technical University of Communications and Informatics, Moscow 123423, Russia;Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia;

关键词: Wigner function;    Harmonic oscillator;    Wave equation;    Exact solution;    Moyal equation;    Rigorous result;   

DOI  :  

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown