# The Stark Effect with Minimum Length

## TL;DR

This paper investigates how a minimal length deformation of the Heisenberg algebra affects the Stark effect in hydrogen, providing theoretical estimates of energy level corrections due to quantum gravity-inspired modifications.

## Contribution

It introduces a perturbative analysis of the Stark effect incorporating minimum length corrections, extending previous hydrogen atom studies to include electric field effects.

## Key findings

- Estimated energy level shifts due to minimum length in Stark effect
- Perturbative corrections for non-degenerate and degenerate states
- Quantitative bounds on minimum length effects in hydrogen

## Abstract

We will study the splitting in the energy spectrum of the hydrogen atom subjected to a uniform electric field (Stark effect) with the Heisenberg algebra deformed leading to the minimum length. We will use the perturbation theory for cases not degenerate ($n=1$) and degenerate ($n=2$), along with known results of corrections in these levels caused by the minimum length applied purely to the hydrogen atom, so that we may find and estimate the corrections of minimum length applied to the Stark effect.