l-states solutions for the q-deformed Scarf potential with path integrals formulation

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.

A precise estimation for vibrational energies of diatomic molecules using the improved Rosen–Morse potential

“… 64 , 65 . The findings of these comparisons show that they coincide with the other potential models 63 – 65 . The vibrational energies for the N ( ) molecule are listed in Table 4 compared to the observed RKR data and the outcomes of Refs.…”

“…The vibrational energies of the ScI ( ) molecule are displayed in Table 3 , along with comparisons to the findings of Refs. 63 – 65 . Diaf et al employed the path integrals formalism to compute the vibrational energies of the ScI ( ) molecule with the q-deformed Scarf potential in Ref.…”

“…Diaf et al employed the path integrals formalism to compute the vibrational energies of the ScI ( ) molecule with the q-deformed Scarf potential in Ref. 63 . While the modified forms of the generalised Mobius square and hyperbolical-type potentials were used in Refs.…”

Feynman kernel analytical solutions for the deformed hyperbolic barrier potential with application to some diatomic molecules

“…For such potentials, the Schrödinger, Klein-Gordon, and Dirac equations are exactly solved for the s-states ℓ ( ) 0 = [22][23][24]. For the bound states ℓ ( ) 0 ¹ , various approximate analytical methods have been proposed: the function analysis ( ) FA [25], the Nikiforov-Uvarov method ( ) NU [26,27], the asymptotic iteration method ( ) AIM [28,29], and the Feynman path integrals formalism ( ) FPI [30][31][32]. In the framework of non-relativistic quantum mechanics, we solve the Feynman Kernel with the deformed hyperbolic barrier potential (DHB) [33]…”

Relativistic energies for the q-deformed Scarf potential with Feynman path integrals formulation

“…Motivated by the success in obtaining approximate bound state solutions of the Feynman Kernel in nonrelativistic case with different forms of exponential potentials [32][33][34][35][36][37][38], we investigate the relativistic bound state solutions of the q-deformed hyperbolic Scarf potential by solving the Dirac equation approximately for arbitrary spin-orbit quantum number κ using an improved approximation scheme to deal with the pseudo centrifugal term under the conditions of the spin symmetry. Furthermore, we examine the effect of a Coulomb-like Tensor interaction on the q-deformed hyperbolic Scarf potential via the bound state solutions of the Dirac equation under the spin a symmetry.…”