# One-dimension quantum systems in the framework of the most general deformation GUP form

## TL;DR

This paper explores the effects of a comprehensive Generalized Uncertainty Principle on one-dimensional quantum systems, including potential wells, barriers, and hydrogen atoms, revealing how deformation influences their energy spectra and wave functions.

## Contribution

It introduces a detailed GUP framework applied to various 1D quantum systems, providing new insights into deformation effects on energy corrections and atomic phenomena.

## Key findings

- Energy corrections for linear potential computed
- Deformation impacts on delta potentials analyzed
- Stark effect modifications observed in 1D hydrogen atoms

## Abstract

This paper provides a concise overview of the comprehensive version of the Generalized Uncertainty Principle (GUP) derived from nonlocal quantum mechanics and extensively addressed by S. Masood, et al. We utilize the specific constraint of this GUP formulation to compute the energy correction and the modified wave function for the linear potential in one dimension. In addition, we examine the impact of deformation on a one-dimensional delta potential well and a one-dimensional delta potential barrier. Furthermore, we specifically focus on the impact of deformation on hydrogen atoms existing in one dimension, and we conduct a distinct investigation into the Stark effect on the atom.