Scattering solution of Schr\"odinger equation with $\delta$-potential in deformed space with minimal length

TL;DR

This paper solves the Schrödinger equation with a delta potential in a deformed space with minimal length, revealing resonance effects and sensitivity to deformation functions.

Contribution

It provides exact bound and scattering solutions for the delta potential in deformed space, highlighting the impact of minimal length on quantum scattering phenomena.

Findings

Resonance energy causes complete wave reflection.

Reflection effects are highly sensitive to deformation function.

Exact solutions are obtained in quasiposition representation.

Abstract

We consider the Dirac $\delta$-function potential problem in general case of deformed Heisenberg algebra leading to the minimal length. Exact bound and scattering solutions of the problem in quasiposition representation are presented. We obtain that for some resonance energy the incident wave is completely reflected. We conclude that this effect is very sensitive to the choice of the deformation function.