Diatomic Molecules in deSitter and Anti-deSitter Spaces

TL;DR

This paper analytically solves the Schr"odinger equation for diatomic molecules in deSitter and anti-deSitter spaces, revealing how spatial deformation affects bound states and establishing experimental bounds on this deformation.

Contribution

It provides exact solutions for diatomic molecules in curved spacetime using the Nikiforov-Uvarov method, incorporating the extended uncertainty principle.

Findings

Derived analytical energy eigenvalues for the system

Provided explicit eigenfunctions in terms of special polynomials

Established an upper limit for the spatial deformation parameter

Abstract

The Schr\"odinger equation for diatomic molecules in deSitter and anti-deSitter spaces is studied using the extended uncertainty principle formulation. The equations are solved by the Nikiforov-Uvarov method for both the Kratzer potential and the pseudoharmonic oscillator. The energy eigenvalues of the system have been derived analytically, and the exact expressions of the eigenfunctions are provided in terms of Romanovski and Jacobi polynomials. The impact of the spatial deformation parameter on the bound states is also examined, with experimental results used to establish an upper limit for this parameter.