Deformed Heisenberg Algebra with a minimal length: Application to some molecular potentials

TL;DR

This paper explores a deformed Heisenberg algebra introducing a minimal length scale, analyzing its impact on molecular potentials and comparing theoretical predictions with experimental data for hydrogen molecules.

Contribution

It applies a deformed quantum mechanics framework to molecular potentials, deriving energy spectra and molecular constants, and estimates the minimal length scale from experimental data.

Findings

Minimal length affects vibrational and rotational energy levels.

Theoretical spectra show good agreement with experimental data.

Estimated minimal length scale is within a certain order of magnitude.

Abstract

We review the essentials of the formalism of quantum mechanics based on a deformed Heisenbeg algebra, leading to the existence of a minimal length scale. We compute in this context, the energy spectra of the pseudoharmonic oscillator and Kratzer potentials by using a perturbative approach. We derive the molecular constants, which characterize the vibration--rotation energy levels of diatomic molecules, and investigate the effect of the minimal length on each of these parameters for both potentials. We confront our result to experimental data for the hydrogen molecule to estimate an order of magnitude of this fundamental scale in molecular physics.