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Physica Scripta

SU (1,1) the hidden dynamical symmetry group for an exact bound state of the Hulthen potential

Woyengipere Oluwaseun Etebu

Published Jun 21, 2022• 0 citations
Publisher

Abstract

Abstract In this research work, an exact normalised bound eigenstate and energy eigenvalue of the Hulthen potential, for the zero angular momentum within the framework of the non-relativistic time independent Schrödinger wave equation were obtained using the Nikiforov–Uvarov method. Also, their self-adjoint differential creation and annihilation (ladder) operators were derived, andfrom the commutation relations their Casimir operator was defined. These results showed that the non-compact S U ( 1 , 1 ) group is the dynamical group for this exact bound state, described by the representation D + ( i ) with a spectrum bounded below.

DOI
10.1088/1402-4896/ac7ae7

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Abstract In this research work, an exact normalised bound eigenstate and energy eigenvalue of the Hulthen potential, for the zero angular momentum within the framework of the non-relativistic time independent Schrödinger wave equation were obtained using the Nikiforov–Uvarov method. Also, their self-adjoint differential creation and annihilation (ladder) operators were derived, andfrom the commutation relations their Casimir operator was defined. These results showed that the non-compact S U ( 1 , 1 ) group is the dynamical group for this exact bound state, described by the representation D + ( i ) with a spectrum bounded below.
BOUND-STATES OF A SEMI-RELATIVISTIC EQUATION FOR THE PT{\cal PT}PT-SYMMETRIC GENERALIZED HULTHÉN POTENTIAL BY THE NIKIFOROV–UVAROV METHOD
The one-dimensional semi-relativistic equation has been solved for the [Formula: see text]-symmetric generalized Hulthén potential. The Nikiforov–Uvarov (NU) method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type, is used to obtain exact energy eigenvalues and corresponding eigenfunctions. We have investigated the positive and negative exact bound states of the s-states for different types of complex generalized Hulthén potentials.
In this paper, the analytical solutions of the [Formula: see text]-dimensional hyper-radial Schrödinger equation are studied in great detail for the Hulthén potential. Within the framework, a novel improved scheme to surmount centrifugal term, the energy eigenvalues and corresponding radial wave functions are found for any [Formula: see text] orbital angular momentum case within the context of the Nikiforov–Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. In this way, based on these methods, the same expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transforming each other is demonstrated. The energy levels are worked out and the corresponding normalized eigenfunctions are obtained in terms of orthogonal polynomials for arbitrary [Formula: see text] states for [Formula: see text]-dimensional space.
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.
In this paper, the bound state solution of the modified Klein–Fock–Gordon equation is obtained for the Hulthén plus ring-shaped-like potential by using the developed scheme to overcome the centrifugal part. The energy eigenvalues and corresponding radial and azimuthal wave functions are defined for any [Formula: see text] angular momentum case on the conditions that scalar potential is whether equal and nonequal to vector potential, the bound state solutions of the Klein–Fock–Gordon equation of the Hulthén plus ring-shaped-like potential are obtained by Nikiforov–Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. The equivalent expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformations to each other is revealed owing to both methods. The energy levels and the corresponding normalized eigenfunctions are represented in terms of the Jacobi polynomials for arbitrary [Formula: see text] states. A closed form of the normalization constant of the wave functions is also found. It is shown that the energy eigenvalues and eigenfunctions are sensitive to [Formula: see text] radial and [Formula: see text] orbital quantum numbers.
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.