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Non-relativistic bound state solutions of a linear combination of deformed Hulthén plus generalized Kratzer potentials using Feynman path integral approach

M. A. Sadoun, Fouzi Haddad

Published Apr 19, 2023• 0 citations
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Abstract

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.

DOI
10.21203/rs.3.rs-2819270/v1

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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.
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The Green’s function for a Klein–Gordon particle under the action of vector plus scalar deformed Hulthén and Woods–Saxon potentials is evaluated by exact path integration. Explicit path integration leads to the Green’s function for different shapes of the potentials. From the singularities of the latter Green’s function, the bound states are extracted. For q≥1 and (1/α)ln q<r<∞, the analytic expression of the energy spectrum and the normalized wave functions for the l states are obtained within the framework of an approximation to the centrifugal term. When the deformation parameter q is 0<q<1 or q<0, it is found that the quantization conditions are transcendental equations involving the hypergeometric function that require a numerical solution for the s-state energy levels. Particular cases of these potentials are also discussed briefly.
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.
We study the nonrelativistic Schrödinger equation for q-deformed Hulthen plus modified inversely quadratic Yukawa potential using the generalized parametric form of NIkiforov-Uvarov method. The energy eigenvalues and the corresponding normalized wave functions expressed in terms of hypergeometric function are obtained. We have also discussed four (4) special cases of this potential, i.e. Woods-Saxon, Hulthen, Morse and inversely quadratic potentials. Keywords: Nonrelativistic Schrödinger equation, q-deformed Hulthen potential, modified inversely quadratic Yukawa potential, parametric Nikiforov-Uvarov method.
In this work, we obtained an approximate bound state solution to Schrodinger with Hulthen plus exponential Coulombic potential with centrifugal potential barrier using parametric Nikiforov-Uvarov method.We obtained both the eigen energy and the wave functions to non -relativistic wave equations.We implement Matlab algorithm to obtained the numerical bound state energies for various values of adjustable screening parameter at various quantum state..The developed potential reduces to Hulthen potential and the numerical bound state energy conform to that of existing literature.
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.