Modified spectral method in phase space: Calculation of the Wigner function. II. Generalizations

We generalize our modified spectral method for the solution of the coupled real partial differential equations in phase space for the stationary Wigner function of an energy eigenstate. This generalization allows us to apply our algorithm to arbitrary high-order partial derivatives without increasing the numerical costs. This is possible since we can derive a sum factorization formula converting a multiple sum into a simple product. We apply our method to evaluate the Wigner function of the Morse oscillator and an asymmetric double-well potential, and compare our results with the exact solution when it is known.