Study of the Wigner Function Computed by Solving the Schrödinger Equation

In this work, we compute the Wigner distribution function from wavefunctions generated by solving the Schrodinger equation. Our goal is to propose an avenue of research that may help better understand certain limitations of Wigner transport equation solvers, such as negative charge densities or limited charge drop-offs in presence of potential barriers. We evaluate the numerical accuracy required by the Schrodinger solver to compute the Wigner function and compare the performance of an analytic and a numerical solver applied to a constant potential profile, as well as to single- and double-barrier structures. Finally, we use the Schrodinger solver to better understand certain conditions to be applied to Wigner transport equation solvers, namely the minimum contact length and k-grid range.