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Eclética Química

Effect of the deformation parameter on the nonrelativistic energy spectra of the q-deformed Hulthen-quadratic exponential-type potential

P. O. Ushie, Ofem Egbe Ubi, Collins Okon Edet, A. N. Ikot

Published Oct 1, 2021• 10 citations
Publisher

Abstract

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.

DOI
10.26850/1678-4618eqj.v46.4.2021.p60-73

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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 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.
This study explores the influence of deformation parameters on quantum information measures using the q-deformed Hulthén-quadratic exponential-type potential. By solving the Schrödinger equation with the parametric Nikiforov-Uvarov (pNU) method, the energy spectrum and wavefunctions were derived. Quantum information measures, including Shannon entropy and Fisher information, were analyzed for ground states in position and momentum spaces. The results validate the Berkner, Bialynicki-Birula, and Mycieslki, and Stam-Cramér-Rao inequalities, underscoring their consistency with quantum principles. These findings deepen our understanding of deformation effects on quantum systems and offer potential applications in astrophysics and quantum chemistry, advancing the exploration of molecular systems and quantum information theory.
In this study, we obtained bound state solutions of the radial Schrödinger equation by the superposition of Hulthén plus Hellmann potential within the framework of Nikiforov-Uvarov (NU) method for an arbitrary - states. The corresponding normalized wave functions expressed in terms of Jacobi polynomial for a particle exposed to this potential field was also obtained. The numerical energy eigenvalues for different quantum state have been computed. Six special cases are also considered and their energy eigenvalues are obtained. Our results are found to be in good agreement with the results in literature. The behavior of energy in the ground and excited state for different quantum state are studied graphically.
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.