Browsing by Author "Ghobrini, Amina"

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Dynamic study of certain non-relativistic and relativistic problems using the path integral approach
(Université M'Hamed Bougara Boumerdès : Faculté des Sciences, 2025) Ghobrini, Amina; Boukabcha, Hocine(Directeur de thèse)
In this thesis, it was proved that the formulation of the Feynman path integral plays an important role in solving relativistic and non-relativistic problems in quantum mechanics. To this end, an approximation scheme for the centrifugal term and an appropriate space time of the Duru-Kleinert transformation allow the radial path integral to be converted into a manageable integral. The first part focuses on the prediction of the non-relativistic ro-vibrational energy for the q-deformed modified P?schl-Teller potential, followed by two special cases including the P?schl-Teller type potential and the generalized hyperbolic potential is presented with some diatomic molecules. The predicted values are in better agreement with numerical results and other methods in the literature. The second part deals with the solution of the Klein-Gordon equation under equal scalar and vector modified second type P?schl-Teller potentials. The eigenvalues of the relativistic energy are positive on the basis of a specific condition for the wave functions. In the third part, we solve the Dirac equation for an arbitrary spin-orbit quantum number ? using the q-deformed generalisedP?schl-Teller potential (q-DGPT). The results of the numerical analysis show that there are only bound states with negative energy in the pseudospin symmetry situation with constraint . Moreover, in the non-relativistic limits, the expression for the non-relativistic ro-vibrational energy of the diatomic molecule is derived from the relativistic energy equation in spin symmetry. The results obtained for 39K2 (a3?+u)and CO (X1?+)under Varshni conditions are in good agreement with theoretical and experimental data
Energy spectra with the Dirac equation of the q-deformed generalized Pöschl-Teller potential via the Feynman approach for 39K2a3∑u+
(Springer Nature, 2024) Ghobrini, Amina; Boukabcha, Hocine; Ami, Ismahane
Context: The diatomic molecules of potassium 39K2a3∑u+ is widely used in industrial chemicals and alternative energy. Besides that, 39K2a3∑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 (DGPT). 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 39K2a3∑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 (DGPT) model is a very consistent model to study and characterize diatomic molecules.
Klein-Gordon equation in higher dimensions via Feynman propagator with the modified second type Pöschl-Teller potential
(Springer, 2024) Ghobrini, Amina; Boukabcha, Hocine; Ami, Ismahane
Recently, the Feynman approach has been used to study the solution of the D-dimensional Klein-Gordon equation under equal scalar and vector modified second type Pöschl-Teller potentials. Approximation has been made to the centrifugal term and space-time transformation is used to deal easily with the difficult computation problem. We found that there are positive energy states for bound states based on the condition for the wave functions. The results are in agreement with those obtained by using other methods found in the literature.
Non-relativistic treatment of q-deformed modified Pöschel Teller potential via path integral approach
(Springer, 2024) Ghobrini, Amina; Boukabcha, Hocine; Ami, Ismahane
This study aims to evaluate the D-dimension Feynman propagator to find the spectrum of non-relativistic energies and the corresponding wavefunctions of the ′ ′ℓ′ ′ states for the q-deformed modified Pöschl-Teller potential. We propose an approximation scheme for the centrifugal term of our potential. In addition, an appropriate space-time of Duru-Kleinert transformation has also been performed to convert the radial path integral into a manageable one. Furthermore, two special cases are to be considered, the Pöschl-Teller type potential and the generalized hyperbolic potential, as well as by a combination of illustration and comparison of some diatomic molecules, namely (HCL, NiC, CO, and I2). It is found that this study is substantially marked, which communicated many important methods for solving the Schrödinger’s equation.
Path integral solutions of the Dirac equation with spin symmetry for the generalized Pöschl–Teller model: modeling the COX1∑+ molecule
(Springer Science and Business Media, 2025) Ghobrini, Amina; Boukabcha, Hocine; Ami, Ismahane; Hajigeorgiou, Photos G.
We solve the Dirac equation with the generalized Pöschl–Teller potential (GPT), using the Feynman path integral formalism and then a Pekeris-like approximation to deal with the centrifugal term, and obtain the relativistic and non-relativistic ro-vibrational energy equations for diatomic molecules. In non-relativistic limits, an application of the carbon monoxide molecule in the ground states, mean absolute percentage deviations from experimental RKR and DPF data were obtained. Furthermore, taking into account the binding energy condition the maximum possible rotations for each vibrational quantum number of CO were calculated. We have shown that our results are in good agreement with the data available in the literature (theoretical and experimental data) on COX1∑+ and that GPT is a very robust model for discussing diatomic molecules