  Nonlocal modeling has drawn more and more attention and becomes steadily more
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 the interaction between point charges
in quantum science. The nonlocal nature of the Wigner equation is fully
exploited to convert the singular potential into the Wigner kernel with weak or
even no singularity, and thus highly accurate numerical approximations are
achievable, which are hardly designed when the singular potential is taken into
account in the local Schr\"odinger equation. The Dirac delta function, the
logarithmic, and the inverse power potentials are considered. Numerically
converged Wigner functions under all these singular potentials are obtained
with an operator splitting spectral method, and display many interesting
quantum behaviors as well.
