On Quantum Tunneling of a Singular Potential

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