Abstract
In this paper, we solve the Feynman Kernel for the q-deformed hyperbolic Scarf potential for any ℓ-states. We propose an accurate generalization of the Pekeris approximation of the centrifugal term adapted to deformed potentials which allows to transform our potential to a solvable shifted modified Pöschl-Teller one. Analytical expressions of the energy spectrum and the normalized ℓ-state eigenfunctions are derived from the Green function. We evaluate and compare our results to the literature. Furthermore, we apply our method in chemical physics to derive the spectrum of some diatomic molecules. We obtained good results compared to state-of-the-art competing analytical and numerical methods.
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