| Resumen |
We delve into the intricacies of the hyperbolic Pöschl–Teller potential, often referred to as the 2nd Pöschl–Teller potential (PTP), and explore its implications on the Schrödinger equation for arbitrary l state case. This exploration encompasses a comprehensive review of various methodologies employed in studying the exact solutions of the S wave scenario, along with approximations concerning the centrifugal term within the radial equation for the arbitrary l setup. Our investigation yields exact solutions for the quasi-exact arbitrary l state model. We achieve this by employing a novel approach rooted in Fuchsian differential equations, thereby presenting a potential solution for the S wave case as well. This innovative method holds promise, particularly in seeking solutions for the Schrödinger equation involving non-trivial potentials where exact solutions remain elusive. © 2024 The Author(s) |
