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International Journal of Quantum Chemistry

Approximate ℓ‐bound state solutions of q‐deformed exponential‐type potentials

José Juan Peña, Jesús García‐Ravelo, Gerardo Ovando, Jesús Morales

Published Feb 17, 2020• 3 citations
Publisher

Abstract

Abstract In this work, the exactly solvable Schrödinger equation for s‐states of a class of multiparameter exponential‐type potential (E‐tP) is used to obtain the approximate ℓ ≠ 0 bound state solutions for the corresponding q‐deformed radial potentials. To deal with the effective potential, the Pekeris approximation for the centrifugal term is applied. The proposal has the advantage that, depending on the choice of the parameters involved in the E‐tP, several q‐deformed exponential potentials are obtained here as particular cases. That is, our proposition indicates that it is not necessary to use specialized methods to solve the Schrödinger equation for specific q‐deformed exponential potentials. At this regard, in order to show the usefulness of the proposed method, we consider the ℓ ≠ 0 bound state solutions of the q‐deformed Tietz, Hulthén, Manning‐Rosen, Shioberg, quadratic exponential, Wei and Hua among other potential models. Furthermore, with the example of the Hua potential we are contributing to solve the recent controversy on the energy spectra of this q‐deformed model. Moreover, in some applications considered in this work the results can be used to correct similar findings already published. Besides, the proposal is useful when considering new q‐deformed potentials with hypergeometric wavefunctions to be used in quantum chemical applications of diatomic molecules.

DOI
10.1002/qua.26189

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Abstract In this work, the exactly solvable Schrödinger equation for s‐states of a class of multiparameter exponential‐type potential (E‐tP) is used to obtain the approximate ℓ ≠ 0 bound state solutions for the corresponding q‐deformed radial potentials. To deal with the effective potential, the Pekeris approximation for the centrifugal term is applied. The proposal has the advantage that, depending on the choice of the parameters involved in the E‐tP, several q‐deformed exponential potentials are obtained here as particular cases. That is, our proposition indicates that it is not necessary to use specialized methods to solve the Schrödinger equation for specific q‐deformed exponential potentials. At this regard, in order to show the usefulness of the proposed method, we consider the ℓ ≠ 0 bound state solutions of the q‐deformed Tietz, Hulthén, Manning‐Rosen, Shioberg, quadratic exponential, Wei and Hua among other potential models. Furthermore, with the example of the Hua potential we are contributing to solve the recent controversy on the energy spectra of this q‐deformed model. Moreover, in some applications considered in this work the results can be used to correct similar findings already published. Besides, the proposal is useful when considering new q‐deformed potentials with hypergeometric wavefunctions to be used in quantum chemical applications of diatomic molecules.
In this article, using an exactly‐solvable multiparameter exponential‐type potential we propose a unified treatment of the analytical bound—state solutions of the Schrödinger equation for exponential‐type potentials in D‐dimensions. Our proposal accepts different approximations to the centrifugal term; however, its usefulness is exemplified in the frame of the Green and Aldrich approach. This fact enables us to compare our results with specific potentials found in the literature and that are obtained here as particular cases of our proposal. That is, instead of solving a specific exponential‐type potential, by resorting each time to a specialized method, the energy spectra and wavefunctions are derived straightforward from the proposed approach. Furthermore, our proposal can be used as an alternative way in the search of solutions to new exponential‐type potentials besides that one can study different approximations to the term . © 2014 Wiley Periodicals, Inc.
In this study, an approximate solution of the Schrödinger equation for the q-deformed Hulthen-quadratic exponential-type potential model within the framework of the Nikiforov–Uvarov method was obtained. The bound state energy equation and the corresponding eigenfunction was obtained. The energy spectrum is applied to study H2, HCl, CO and LiH diatomic molecules. The effect of the deformation parameters and other potential parameters on the energy spectra of the system were graphically and numerically analyzed in detail. Special cases were considered when the potential parameters were altered, resulting in deformed Hulthen potential, Hulthen potential, deformed quadratic exponential-type potential and quadratic exponential-type potential. The energy eigenvalues expressions agreed with what obtained in literature. Finally, the results can find many applications in quantum chemistry, atomic and molecular physics.
We generalize the Pekeris approximation for the centrifugal term potential, l(l+1)r2, and use this to obtain the solutions of the radial Schrödinger equation for the arbitrary angular quantum number, l, of the Hulthén potential. We also obtain the expressions for the bound state energies corresponding to this potential and calculate their values for different states and compare with other results presented in the literature. We also consider some models of physical potentials, namely, the Eckart potential, the Poschl-Teller potentials, the Rosen-Morse potential, the Woods-Saxon potential, and the Manning-Rosen potential. Thus, following straightforward the example corresponding to the Hulthén potential, we show what the radial solutions and the energy spectra for these potentials are.
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.
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.
We present solutions of the Schrodinger equation with superposition of Manning-Rosen plus inversely Mobius square plus quadratic Yukawa potentials using parametric Nikiforov Uvarov method along with an approximation to the centrifugal term. The bound state energy eigenvalues for any angular momentum quantum number l and the corresponding un-normalized wave functions are calculated. The mixed potential which in some particular cases gives the solutions for different potentials: the Manning-Rosen, the Mobius square, the inversely quadratic Yukawa and the Hulthén potentials along with their bound state energies are obtained.