Scattering and Bound State Solutions of Asymmetric Hulth\'{e}n Potential
Altu\u{g} Arda, Oktay Aydo\u{g}du, Ramazan Sever
TL;DR
This paper solves the one-dimensional Schrödinger equation for an asymmetric Hulthén potential, deriving reflection, transmission, and bound state solutions using hypergeometric functions, and confirms unitarity in the non-relativistic regime.
Contribution
It provides exact analytical solutions for scattering and bound states of the asymmetric Hulthén potential using hypergeometric functions.
Findings
Reflection and transmission coefficients derived
Bound state energies obtained
Unitarity condition verified in non-relativistic limit
Abstract
One-dimensional time-independent Schr\"odinger equation is solved for the asymmetric Hulth\'{e}n potential. Reflection and transmission coefficients and bound state solutions are obtained in terms of the hypergeometric functions. It is observed that the unitary condition is satisfied in non-relativistic region.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.