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Physica Scripta

Path integral solution of the Schrödinger equation with a linear combination of deformed Hulthén plus generalized Kratzer potentials: application to diatomic molecules

M. A. Sadoun, Fouzi Haddad, Hamza Adnane, Ahmed Tabouche

Published Jun 9, 2026• 1 citation
Publisher

Abstract

Abstract In this study, we investigated the approximate analytical bound state solutions of the Schrödinger equation, considering a linear combination of the deformed (Hulthén 1942 Ark. Mat. Astron. Fys. 28A 671) potential and the generalized (Kratzer 1920 Z. Phys. 3 289–307) potential. The analysis was performed within the path-integral formalism. Using an appropriate approximation to evaluate the centrifugal term, we derived the energy spectrum and normalized wave functions of the bound states from the poles of the Green’s function and its residues. To evaluate the accuracy and applicability of the derived expressions, we discuss several limiting cases of the potential and carry out numerical calculations of the energy levels, complemented by illustrative plots for selected diatomic molecules.

DOI
10.1088/1402-4896/ae7ac2

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Abstract In this study, we investigated the approximate analytical bound state solutions of the Schrödinger equation, considering a linear combination of the deformed (Hulthén 1942 Ark. Mat. Astron. Fys. 28A 671) potential and the generalized (Kratzer 1920 Z. Phys. 3 289–307) potential. The analysis was performed within the path-integral formalism. Using an appropriate approximation to evaluate the centrifugal term, we derived the energy spectrum and normalized wave functions of the bound states from the poles of the Green’s function and its residues. To evaluate the accuracy and applicability of the derived expressions, we discuss several limiting cases of the potential and carry out numerical calculations of the energy levels, complemented by illustrative plots for selected diatomic molecules.
Abstract The approximate bound state solutions of Schrödinger equation with linear combination of a q-deformed Hulthén potential plus screened Kratzer potential were obtained with the help of appropriate approximation to evaluate the centrifugal term. The Feynman path integral approach was used to obtain the analytical solutions. The energy spectrum and the normalized wave functions of the bound states are derived from the poles of the Green’s function and its residues. Particular cases of these potentials are also discussed briefly and it is found that obtained results are in good agreement with those obtained in the literature.
In this paper, we investigate the approximate analytical bound states with a linear combination of two diatomic molecule potentials, Yukawa and four parameters potentials, within the framework of the path integral formalism. With the help of an appropriate approximation to evaluate the centrifugal term, the energy spectrum and the normalized wave functions of the bound states are derived from the poles of Green's function and its residues. The partition function and other thermodynamic properties were obtained using the compact form of the energy equation.
Abstract The equation of Schrodinger is a fundamental mathematical framework used to clarify the motion of the wave form, which is a phenomenon in the field of quantum physics. A method's wave function contains the complete description of its particles. The computational solution of the Schrodinger problem is a multifaceted problem. The eigenvalues and typical functions of the modified Kratzer plus Hulthen potential were ascertained analytically in this study. This study used an estimating approach that Nikiforov-Uvarov functional analysis had suggested for dealing with the problem. Estimating energy spectra and applying the results to certain specific diatomic molecules was the aim. The excellent results obtained from this strategy were confirmed by comparing our eigenvalue data with additional numerical data that was gathered by other researchers.
The Schrödinger equation was solved for the Hulthén plus screened Kratzer Potential (HSKP) via the Nikiforov–Uvarov – functional analysis (NUFA) method. The bound-state energy and wave function for the HSKP were obtained in a closed form by applying the Greene–Aldrich approximation scheme to the inverse-square term. Using the resulting energy equation, we computed the energy spectra for 12 diatomic molecules (CuLi, TiH, VH, TiC, HCl, LiH, H2, ScH, CO, I2, N2, and NO) for various quantum states. To show the accuracy of our procedure, four special cases of the collective potential were obtained, and the results are in excellent agreement with the existing literature.
Abstract The equation of Schrodinger is a fundamental mathematical framework used to clarify the motion of the wave form, which is a phenomenon in the field of quantum physics. A method's wave function contains the complete description of its particles. The computational solution of the Schrodinger problem is a multifaceted problem. The eigenvalues and typical functions of the modified Kratzer plus Hulthen potential were ascertained analytically in this study. This study used an estimating approach that Nikiforov-Uvarov functional analysis had suggested for dealing with the problem. Estimating energy spectra and applying the results to certain specific diatomic molecules was the aim. The excellent results obtained from this strategy were confirmed by comparing our eigenvalue data with additional numerical data that was gathered by other researchers.
The problem of a Dirac particle moving in a deformed Hulthén potential is solved in the framework of the path integral formalism. With the help of the Biedenharn transformation, the construction of a closed form for the Green’s function of the second-order Dirac equation is done by using a proper approximation to the centrifugal term and the Green’s function of the linear Dirac equation is calculated. The energy spectrum for the bound states is obtained from the poles of the Green’s function. A Dirac particle in the standard Hulthén potential ( q = 1) and a Dirac hydrogen-like ion ( q = 1 and a → ∞) are considered as particular cases.