Nonlocalization of singular potentials in quantum dynamics

Nonlocal modeling has drawn more and attention becomes steadily powerful in scientific computing. In this paper, we demonstrate the superiority of a first-principle nonlocal model—Wigner function—in treating singular potentials which are often used to model interaction between point charges quantum science. The nature Wigner equation is fully exploited convert potential into kernel with weak or even no singularity, thus highly accurate numerical approximations achievable, hardly designed when taken account local Schrödinger equation. Dirac delta function, logarithmic, inverse power considered. Numerically converged functions under all these obtained fourth-order operator splitting spectral method, display many interesting behaviors as well.