Quantum tunneling of a singular potential
- URL: http://arxiv.org/abs/2102.12789v1
- Date: Thu, 25 Feb 2021 11:21:13 GMT
- Title: Quantum tunneling of a singular potential
- Authors: A. Zh. Muradyan
- Abstract summary: singularity of the potential function makes quantum tunneling problem mathematically underdetermined.
I discuss here how quantum tunneling will behave if the original singular nature of the Schrodinger equation left untuched.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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.
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