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Non-central potential; shape-invariance condition; homogeneous manifold $SL(2,\mathbb{C})/GL(1,\mathbb{C})$; hypergeometric and Laguerre equation

In this study, we are going to obtain the energy spectrum and the corresponding solution of the noncentral Makarov potential. In this case, we consider the arbitrary angular momentum with quantum number l. In order to calculate the energy spectrum and eigenfunction we use the factorisation method. The factorisation methodleads us to discuss the shape-invariance condition with respect to any index as $n$ and $m$. Here, we also achieve the shape invariance with respect to the main quantum number $n$. It leads to the quantum-solvable models on real forms of the homogeneous manifold $SL(2,\mathbb{C})/GL(1,\mathbb{C})$ with infinite-fold degeneracy for $\gamma\upsilon = 0$ and $\gamma\upsilon \neq 0$. These processes also help us to obtain raising and lowering operators of states on the above-mentioned homogeneous manifold.

FARZANEH SAFARI¹

1. College of Mechanics and Materials, Hohai University, Nanjing 211100, China

Published

15 March 2020

Manuscript received

29 July 2019

Manuscript revised

5 November 2019

Accepted

3 February 2020

Early published

Unedited version published online

Final version published online

19 March 2020