Path integral discussion of Scarf-like potentials

Ahmed Diaf, Mohammed Hachama

Abstract In this paper, the Dirac equation with the q-deformed Scarf potential for spin symmetry is solved for an arbitrary spin-orbit quantum number κ, in the presence of Coulomb-like potential tensor. Using the Feynman path integral formalism and the Pekeris approximation of the centrifugal term, we obtain the bound state energy eigenvalues and the associated spinor of the Dirac particle. Furthermore, this method is used to determine the spectrum of two diatomic molecules Li 2(61Π u ) and KRb(B −1Π). The obtained results are compared to the experimental and numerical ones.

Osvaldo Civitarese, Manuel Gadella

Christian Grosche

Ahmed Diaf, Mohammed Hachama, M M’hamed Ezzine

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.

Nalan Kandırmaz

Bu çalışmada PT Simetrik/ PT Simetrik Hermityen Olmayan q-deformasyonlu Trigonometrik Scarf Potansiyelinin enerji spektrumu ve karşılık gelen dalga fonksiyonu Path İntegral yöntemi kullanılarak elde edildi. Öncelikle bu potansiyelin kerneli parametrik zaman kullanılarak enerji spektrumu ve dalga fonksiyonu cinsinden türetildi. Kernelden elde edilen Green fonksiyonu ile enerji spektrumu ve dalga fonksiyonu gösterildi.

S. N. Storchak