Energy spectra with the Dirac equation of the q-deformed generalized Pöschl-Teller potential via the Feynman approach for 39 K 2 a 3 ∑ u + .

CONTEXT: The diatomic molecules of potassium 39 K 2 a 3 ∑ u + is widely used in industrial chemicals and alternative energy. Besides that, 39 K 2 a 3 ∑ u + is very useful for researching molecular interactions and energy states, especially in the context of quantum chemistry and spectroscopy. In the present work, a newly proposed diatomic potential model within relativistic and non-relativistic quantum mechanics has been considered, to obtain corresponding energy eigenvalues and related normalized eigenfunctions.

METHODS: The Dirac equation has been solved for an arbitrary spin-orbit quantum number κ using the path integral technique with the q -deformed generalized Pöschl-Teller potential ( D G P T ) . By including a Pekeris-type approximation to handle the centrifugal factor, it was possible to obtain the spin and pseudospin-symmetric solution of the relativistic energy eigenvalues and wave equation. To assess the correctness of this work, Maple software was used to present some numerical findings for various values of n and κ . With the constraint λ ~ > η ~ + 1 , it was shown that in the situation of pseudospin symmetry, only bound states exist with negative energy. In the non-relativistic limits, the non-relativistic ro-vibrational energy expression of the diatomic molecule is derived from the relativistic energy equation under spin symmetry. Under Varshni conditions, both vibrational and ro-vibrational energies of the 39 K 2 a 3 ∑ u + molecule were computed and compared with the RKR data. The average absolute percentage deviations from the RKR data obtained for the potassium molecule are 0.5018 % . This demonstrates that the ( D G P T ) model is a very consistent model to study and characterize diatomic molecules.