Vv. Kudryashov, QUASI-HARMONIC APPROXIMATION FOR SOLUTION OF THE BLOCH EQUATION IN THE WIGNER-WEYL REPRESENTATION, Doklady Akademii nauk BSSR, 38(5), 1994, pp. 38-41
The analytic approximation is obtained for the Wigner distribution fun
ction which describes the thermodynamic equilibrium state in the three
-dimensional space. This approximation gives the exact result for the
anisotropic harmonic oscillator and has the correct quasi-classical as
ymptotic behaviour for an arbitrary potential. The iterative procedure
is given to solve the Bloch equation for the Wigner function.