Regularization of $\delta'$ potential in general case of deformed space with minimal length

TL;DR

This paper defines and analyzes the $ abla$ potential in deformed quantum space with minimal length, deriving exact energy levels and eigenfunctions for specific potentials under various deformation functions.

Contribution

It introduces a general definition of the $ abla$ potential in deformed space and provides exact solutions for energy spectra and eigenfunctions for different deformation cases.

Findings

Exact energy levels for $ abla$ and related potentials are derived.

Eigenfunctions are explicitly constructed for deformed space scenarios.

Deformation functions significantly influence the energy spectrum.

Abstract

In general case of deformed Heisenberg algebra leading to the minimal length, we present a definition of the $\delta'(x)$ potential as a linear kernel of potential energy operator in momentum representation. We find exactly the energy level and corresponding eigenfunction for $\delta'(x)$ and $\delta(x)-\delta'(x)$ potentials in deformed space with arbitrary function of deformation. The energy spectrum for different partial cases of deformation function is analysed.