  Singularity of the potential function makes quantum tunneling problem
mathematically underdetermined. To circumvent the difficulties it introduced in
physics, a potential singularity cutoff is often used, followed by a reverse
limit transition, or is a suitable self-adjoint extension of the Hamiltonian
along the entire coordinate axis made. However, both of them somehow affect the
singular nature of the problem, and so I discuss here how quantum tunneling
will behave if the original singular nature of the Schrodinger equation left
untuched. To do this, I use the property of the probability density current
that the singularities are mutually destroyed in it. It is found that the
mildly singular potential has a finite, but unusual tunneling transparency, in
particular, a non-zero value at zero energy of incident particle. The tunneling
of one dimensional Coulomb potential exhibits infinitely fast and complete
oscillation at the zero energy boundary and a suppresion to zero in the
high-energy limit. In the more singular region, the tunneling becomes
forbidden, theby repeating the well-known result of the regularized
counterparts.
