MODIFIED SPECTRAL METHOD IN PHASE-SPACE - CALCULATION OF THE WIGNER FUNCTION - I - FUNDAMENTALS

We present a method for the direct computation of the Wigner function by solving a coupled system of linear partial differential equations. Our procedure is applicable to arbitrary binding potentials. We introd uce a modified spectral tau method that uses Chebyshev polynomials as shape functions to approximate the solution. Since two differential eq uations are solved simultaneously, the resulting linear equation syste m is overdetermined. We approximate its solution by a least-squares me thod. We prove the stability and convergence of our scheme. As an appl ication, we compute numerically the Wigner function for the harmonic o scillator. Our calculations show excellent agreement with known analyt ic results.