# Non-Relativistic and Relativistic Equations for the Kratzer Potential plus a Dipole in 2D Systems

## TL;DR

This paper derives analytical solutions for wave equations in 2D systems with a combined Kratzer and dipole potential, exploring how angular and radial moments influence energy levels across different relativistic and non-relativistic equations.

## Contribution

It provides new analytical expressions for energies and wave functions in 2D for Schrödinger, Klein-Gordon, and Dirac equations with a combined potential, considering spin and pseudo-spin symmetries.

## Key findings

- D_{theta} term tends to dissociate the system.
- D_{r} term can amplify or decrease Coulomb binding.
- Energy dependence on radial and angular moments analyzed.

## Abstract

In this work, we study the wave equations in 2D Euclidian space for a new non-central potential consisting of a Kratzer term and a dipole term. For Schrodinger equation, we obtain the analytical expressions of the energies and the wave functions of the system. For Klein-Gordon and Dirac equations, we do the study in both spin and pseudo-spin symmetries to get the eigenfunctions and the eingenvalues. Then we study the dependence of energies on the radial moment D_{r} and the angular moment D_{theta}. We find that the D_{theta} term tends to dissociate the system, and thus counteracts the Coulomb binding effect, and that the D_{r} term can either amplify or decrease this effect according to its sign.