On the quantum tunneling of one dimensional coulomb singular potential barrier

TL;DR

This paper investigates quantum tunneling through a one-dimensional Coulomb singular potential barrier, revealing unique oscillatory behavior near zero energy and classical transparency at high energies.

Contribution

It demonstrates how Coulomb singularity influences tunneling, showing oscillations in transmission coefficient and transition to regular potential behavior at high energies.

Findings

Oscillations in transmission coefficient near zero energy

Transition to complete transparency at high energies

Coulomb singularity affects tunneling behavior

Abstract

How quantum tunneling will behave when the singularity is preserved as much as possible is the main question of this paper. We get that the Coulomb sibgularity is reflected as infinitly accelerated oscillations in the transmission coefficient between zero and one when the incident particles energy approaches the zero boundary. At relatively high energies, the tunneling acqures the caracter inherent in regular potentials, and becomes completly transparent in the asymptote.