# A short note on "Group theoretic approach to rationally extended shape invariant potentials" [Annals of Physics 359, 46 (2015)]

## TL;DR

This paper establishes the equivalence of compatibility conditions in shape invariant potentials and explores their connection with potential algebra, providing examples involving extended Jacobi and Laguerre potentials.

## Contribution

It demonstrates the equivalence of different compatibility conditions and reinforces the link between shape invariance and potential algebra for extended potentials.

## Key findings

- Proved equivalence of compatibility conditions in shape invariant potentials.
- Reinforced the connection between shape invariance and potential algebra.
- Provided examples with extended Jacobi and Laguerre potentials.

## Abstract

It is proved the equivalence of the compatibility condition of [A. Ramos, J. Phys. A 44 (2011) 342001, Phys. Lett. A 376 (2012) 3499] with a condition found in [Yadav et al., Ann. Phys. 359 (2015) 46]. The link of Shape Invariance with the existence of a Potential Algebra is reinforced for the rationally extended Shape Invariant potentials. Some examples on X1 and Xl Jacobi and Laguerre cases are given.