New method to eliminate cross-term in wigner distribution

Hiroshi Inuzuka, Kouji Murayama, Yasushi Tadauchi

Maurice A. de Gosson, Serge M. de Gosson

V.G. Novitzky

Lorenzo Galleani, Leon W. Cohen

A new method is presented to study systems governed by ordinary linear differential equations and partial differential equations whose solutions are waves. We show that one can obtain a differential equation for the Wigner distribution of the solution of a dynamical equation of evolution. As an example we derive in a new way the equation governing the Wigner distribution for the Schrodinger equation. We also consider differential equations where the forcing terms are random processes.

Amalia Torre

Sh. M. Nagiyev, A. M. Jafarova, E. I. Jafarov

We propose a phase-space representation concept in terms of the Wigner function for a quantum harmonic oscillator model that exhibits the semiconfinement effect through its mass varying with the position. The new method is used to compute the Wigner distribution function exactly for such a semiconfinement quantum system. This method suppresses the divergence of the integrand in the definition of the quantum distribution function and leads to the computation of its analytical expressions for the stationary states of the semiconfined oscillator model. For this quantum system, both the presence and absence of the applied external homogenous field are studied. Obtained exact expressions of the Wigner distribution function are expressed through the Bessel function of the first kind and Laguerre polynomials. Furthermore, some of the special cases and limits are discussed in detail.