Scattering problem in deformed space with minimal length

TL;DR

This paper explores how a minimal length scale, arising from a deformed Heisenberg algebra, affects elastic scattering, deriving key quantities like Green's functions, scattering amplitudes, and cross-sections for various potentials.

Contribution

It introduces a framework for scattering in deformed space with minimal length and computes scattering parameters for Yukawa and Coulomb potentials.

Findings

Derived Green's function for free particles in deformed space

Calculated scattering amplitudes and cross-sections in deformed space

Analyzed effects of minimal length on scattering processes

Abstract

We investigated the elastic scattering problem with deformed Heisenberg algebra leading to the existence of a minimal length. The continuity equations for the moving particle in deformed space were constructed. We obtained the Green's function for a free particle, scattering amplitude and cross-section in deformed space. We also calculated the scattering amplitudes and differential cross-sections for the Yukawa and the Coulomb potentials in the Born approximation.