MODIFIED SPECTRAL METHOD IN PHASE-SPACE - CALCULATION OF THE WIGNER FUNCTION - II - GENERALIZATIONS

We generalize our modified spectral method for the solution of the cou pled real partial differential equations in phase space for the statio nary Wigner function of an energy eigenstate. This generalization allo ws us to apply our algorithm to arbitrary high-order partial derivativ es without increasing the numerical costs. This is possible since we c an derive a sum factorization formula converting a multiple sum into a simple product. We apply our method to evaluate the Wigner function o f the Morse oscillator and an asymmetric double-well potential, and co mpare our results with the exact solution when it is known.