Study on energy and information-entropic measures of Hulthén potential in D dimension by an intuitive approximation to centrifugal term

Energy spectrum as well as various information theoretic measures are considered for Hulthén potential in D dimension. For a given ℓ≠0 state, analytic expressions are derived, following a simple intuitive approximation for accurate representation of centrifugal term, within the conventional Nikiforov-Uvarov method. This is derived from a linear combination of two widely used Greene-Aldrich and Pekeris-type approximations. Energy, wave function, normalization constant, expectation value in r and p space, Heisenberg uncertainty relation, entropic moment of order α¯, Shannon entropy, Rényi entropy, disequilibrium, majorization as well as four selected complexity measures like LMC (López-Ruiz, Mancini, Calbert), shape Rényi complexity, Generalized Rényi complexity and Rényi complexity ratio are offered for different screening parameters (δ). The effective potential is described quite satisfactorily throughout the whole domain. Obtained results are compared with theoretical energies available in literature, which shows excellent agreement. Performance of six different approximations to centrifugal term is critically discussed. An approximate analytical expression for critical screening for a specific state in arbitrary dimension is offered. Additionally, some inter-dimensional degeneracy occurring in two states, at different dimension for a particular δ is also uncovered. PACS: 02.60.-x, 03.65.Ca, 03.65.Ge, 03.65.-w Keywords: Hulthén potential, Rényi complexity ratio, Statistical complexity, Majorization, Pekeris approximation, Greene-Aldrich approximation.

Morse potential in relativistic contexts from generalized momentum operator: Schottky anomalies, Pekeris approximation and mapping

In this work, we explore a generalization of the Dirac and Klein–Gordon (KG) oscillators, provided with a deformed linear momentum inspired in nonextensive statistics, that gives place to the Morse potential in relativistic contexts by first principles. In the (1 + 1)-dimensional case, the relativistic oscillators are mapped into the quantum Morse potential. Using the Pekeris approximation, in the (3 + 1)-dimensional case, we study the thermodynamics of the S-waves states (l = 0) of the H2, LiH, HCl and CO molecules (in the non-relativistic limit) and of a relativistic electron, where Schottky anomalies (due to the finiteness of the Morse spectrum) and spin contributions to the heat capacity are reported. By revisiting a generalized Pekeris approximation, we provide a mapping from (3 + 1)-dimensional Dirac and KG equations with a spherical potential to an associated one-dimensional Schrödinger-like equation, and we obtain the family of potentials for which this mapping corresponds to a Schrödinger equation with non-minimal coupling.

Nuclear energy excitation by Bohr Hamiltonian for triaxial nuclei using Killingbeck plus Morse potential

This paper proposes an improved potential for the [Formula: see text]-part of the collective Bohr Hamiltonian, namely, a Killingbeck plus Morse potential, while the [Formula: see text]-part is solved for a triaxial deformation close to [Formula: see text]. The Asymptotic Iteration Method is used, involving the Pekeris approximation, to calculate the energy eigenvalues and the eigenfunctions after an exact separation of the Bohr Hamiltonian into its variables is achieved. The results of these calculations are applied for energy spectra of the low-lying states and for corresponding [Formula: see text] quadrupole transition probabilities of the [Formula: see text] isotopes. Moreover, the results of the present solution are compared with those of the well-known [Formula: see text] and [Formula: see text] models.

The bound state solutions of the D-dimensional Schrödinger equation for the Woods–Saxon potential

In this work, the analytical solutions of the [Formula: see text]-dimensional radial Schrödinger equation are studied in great detail for the Wood–Saxon potential by taking advantage of the Pekeris approximation. Within a novel improved scheme to surmount centrifugal term, the energy eigenvalues and corresponding radial wave functions are found for any angular momentum case within the context of the Nikiforov–Uvarov (NU) and Supersymmetric quantum mechanics (SUSYQM) methods. In this way, based on these methods, the same expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformed each other is demonstrated. In addition, a finite number energy spectrum depending on the depth of the potential [Formula: see text], the radial [Formula: see text] and orbital [Formula: see text] quantum numbers and parameters [Formula: see text] are defined as well.

Closed Analytical Solutions of the D-Dimensional Schrödinger Equation with Deformed Woods–Saxon Potential Plus Double Ring-Shaped Potential

By employing the Pekeris approximation, the D-dimensional Schrödinger equation is solved for the nuclear deformed Woods–Saxon potential plus double ring-shaped potential within the framework of the asymptotic iteration method (AIM). The energy eigenvalues are given in a closed form, and the corresponding normalised eigenfunctions are obtained in terms of hypergeometric functions. Our general results reproduce many predictions obtained in the literature, using the Nikiforov–Uvarov method (NU) and the improved quantisation rule approach, particularly those derived by considering Woods–Saxon potential without deformation and/or without ring shape interaction.

Scattering State of Coupled Hulthen–Woods–Saxon Potentials for the Duffin–Kemmer–Petiau Equation with Pekeris Approximation for the Centrifugal Term

We studied the approximate analytical scattering state of the Duffin–Kemmer–Petiau (DKP) equation for arbitrary l-state for couple Hulthen–Woods–Saxon potential using the Pekeris approximation for the centrifugal term. We obtained an energy spectrum, normalised radial wave functions of the scattering states, and the corresponding formula for the phase shifts, which is derived in detail. Special cases of Hulthen and Woods–Saxon potentials were also studied.

Spin and Pseudospin Symmetry in Generalized Manning-Rosen Potential

Spin and pseudospin symmetric Dirac spinors and energy relations are obtained by solving the Dirac equation with centrifugal term for a new suggested generalized Manning-Rosen potential which includes the potentials describing the nuclear and molecular structures. To solve the Dirac equation the Nikiforov-Uvarov method is used and also applied the Pekeris approximation to the centrifugal term. Energy eigenvalues for bound states are found numerically in the case of spin and pseudospin symmetry. Besides, the data attained in the present study are compared with the results obtained in the previous studies and it is seen that our data are consistent with the earlier ones.

GALILEAN COVARIANT DIRAC EQUATION WITH A WOODS–SAXON POTENTIAL

We derive and solve the Galilean covariant Dirac equation, also called "Lévy-Leblond equation", for spin-½ particles in a Woods–Saxon potential. We obtain this wave equation with a Galilean covariant approach, which is based on a (4+1)-dimensional manifold with light-cone coordinates followed by a reduction to the (3+1)-dimensional Galilean space-time. We apply the Pekeris approximation and exploit the Nikiforov–Uvarov method to find the energy eigenvalues and eigenfunctions.

SEMI-RELATIVISTIC SOLUTIONS OF THE TWO-BODY SPINLESS SALPETER EQUATION UNDER THE WOODS–SAXON POTENTIAL AND THE PEKERIS APPROXIMATION

In this paper, by applying the Pekeris approximation and in the frame of Supersymmetric Quantum Mechanics (SUSYQM), the semi-relativistic solutions of the two-body spinless Salpeter equation are obtained analytically. For an interaction of nuclear form, we obtain the approximate bound-state energy eigenvalues and the corresponding wave functions using the shape invariance concept. The solutions are reported for any l state and some energy eigenvalues are given. These results are useful in elementary-particle physics and nuclear physics to obtain the bound states spectra of relativistic systems such as fermion–antifermion systems.