Narrow Results

In this paper, we show an alternative and accurate solution of the radial Schrödinger equation for the exponential cosine screened Coulomb potential within the framework of the asymptotic iteration method. Unlike other methods, which require approximations for the centrifugal or exponential terms, we show that it is possible to solve the full potential without making any approximations within the framework of this method. The bound state energy eigenvalues are obtained for any n and l values and the results are compared with the findings of different methods for several screening parameters. Moreover, we study the screening parameter δ = 0 case to obtain the energy eigenvalues and corresponding eigenfunctions of this potential in a closed-form.

This paper presents an open-source program called AIMpy built on Python language. AIMpy is a solver for Schrödinger-like differential equations using asymptotic iteration method (AIM). To confirm that the code works seamlessly, it has been shown through the paper, with recalculation of some previously studied eigenvalue examples, that the code can very well reproduce their results.

By using the asymptotic iteration method, we have calculated numerically the eigenenergies E_n of Razavy potential V(x) = (ζ cosh 2x-M)². The calculated eigenenergies are identical with known values in the literature. Finally, the non-quasi-exactly solvable eigenenergies of Razavy potential for the highest excited states are numerically determined. Some new results for arbitrary parameter M also presented.

In this paper, we investigate the exact bound state solution of the Klein–Gordon equation for an energy-dependent Coulomb-like vector plus scalar potential energies. To the best of our knowledge, this problem is examined in literature with a constant and position dependent mass functions. As a novelty, we assume a mass-function that depends on energy and position and revisit the problem with the following cases: First, we examine the case where the mixed vector and scalar potential energy possess equal magnitude and equal sign as well as an opposite sign. Then, we study pure scalar and pure vector cases. In each case, we derive an analytic expression of the energy spectrum by employing the asymptotic iteration method. We obtain a nontrivial relation among the tuning parameters which lead the examined problem to a constant mass one. Finally, we calculate the energy spectrum by the Secant method and show that the corresponding unnormalized wave functions satisfy the boundary conditions. We conclude the paper with a comparison of the calculated energy spectra versus tuning parameters.

In this paper, we study the effect of the constant magnetic field on energy levels of the Dirac particles such as electron, proton and heavy ions. We calculate the energy eigenvalues of the Dirac equation in the presence of the magnetic field and two-dimensional harmonic oscillator potential with spin symmetry by using the supersymmetric quantum mechanics and asymptotic iteration methods.

The asymptotic iteration method is used for Dirac and Klein–Gordon equations with a linear scalar potential to obtain the relativistic eigenenergies. A parameter, ς = 0, 1, is introduced in such a way that one can obtain Klein–Gordon bound states from Dirac bound states. It is shown that this method asymptotically gives accurate results for both Dirac and Klein–Gordon equations.

The asymptotic iteration method is used to calculate the eigenenergies for the asymmetrical quantum anharmonic oscillator potentials , with (α = 2) for quartic, and (α = 3) for sextic asymmetrical quantum anharmonic oscillators. An adjustable parameter β is introduced in the method to improve its rate of convergence. Comparing the present results with the exact numerical values, and with the numerical results of the earlier works, it is found that asymptotically, this method gives accurate results over the full range of parameter values A_j.

The eigenvalues of unbounded potential from below of the form , has been obtained over a full range of the parameter values a and b. The calculated results are in complete agreement with exact numerical results obtained by H.-T. Cho and C.-L. Ho. Moreover, we also obtained analytical expression for E_n in the case when b = 0. Some new results for non-quasiexactly solvable case are presented using the asymptotic iteration method.

In this paper, we use the concept of conformable fractional derivative to study the nonrelativistic radial Schrödinger equation. We suggest an extended version of the Cornell potential as the quark–antiquark interaction of light and heavy mesons. We generalize the asymptotic iteration method to the fractional domain. The latter is used to calculate the energy eigenvalues, as well as the effect of the fractional order $\nu$ on energy spectra. To test the applicability of our model, we use the obtained results to reproduce the mass spectra of some light and heavy mesons such as $b\bar{b}$, $c\bar{c}$, $c\bar{s}$, $\bar{b}c$, $b\bar{q}$ and $b\bar{s}$ quarks. The mass spectra are obtained at different values of the fractional order parameter $\nu$ and were compared with experimental results and other relevant theoretical works. Using the wave function, we calculated the decay constants for heavy-light $D^0$, $D^{+}$, $D_s^{+}$, $B^{-}$, ${\bar{B}}^0$ and ${\bar{B}}_s^0$ mesons. Our results are found to be in good agreement with the experimental data, and improved in comparison with other theoretical previsions.

Within the framework of the asymptotic iteration method, we investigate the exact analytical solution for pionic atom in the Coulomb field of a nucleus. Exact bound state energy eigenvalues and corresponding eigenfunctions are determined for the case of angular momentum l≠0, for which the Coulomb potential is exactly solvable. Bound state eigenfunctions solutions, which have been extremely used in applications related with molecular spectroscopy, are obtained in terms of confluent hypergeometric functions.

The analytical expressions for the eigenvalues and eigenvectors of the Klein–Gordon equation for q-deformed Woods–Saxon plus new generalized ring shape potential are derived within the asymptotic iteration method in two cases, namely, the case of equal mixed vector and scalar potentials and the case when the vector potential is chosen to be equal to the q-deformed Woods–Saxon plus the new generalized ring-shaped potential while the scalar one is taken equal to the ring-shaped potential. The latter is considered as a small perturbation. The obtained eigenvalues are given in a closed form and the corresponding normalized eigenvectors, for any l, are formulated in terms of the generalized Jacobi polynomials for the radial part of the Klein–Gordon equation and associated Legendre polynomials for its angular one. When the shape deformation is canceled, we recover the same solutions previously obtained by the Nikiforov–Uvarov method for the standard spherical Woods–Saxon potential. It is also shown that, from the obtained results, we can derive the solutions of this problem for Hulthen potential.

In recent years, an extensive survey on various wave equations of relativistic quantum mechanics with different types of potential interactions has been a line of great interest. In this regime, special attention has been given to the Dirac equation because the spin-½ fermions represent the most frequent building blocks of the molecules and atoms. Motivated by the considerable interest in this equation and its relativistic symmetries (spin and pseudospin), in the presence of solvable potential model, we attempt to obtain the relativistic bound states solution of the Dirac equation with double ring-shaped Kratzer and oscillator potentials under the condition of spin and pseudospin symmetries. The solutions are reported for arbitrary quantum number in a compact form. The analytic bound state energy eigenvalues and the associated upper- and lower-spinor components of two Dirac particles have been found. Several typical numerical results of the relativistic eigenenergies have also been presented. We found that the existence or absence of the ring shaped potential has strong effects on the eigenstates of the Kratzer and oscillator particles, with a wide band spectrum except for the pseudospin-oscillator particles, where there exist a narrow band gap.

In this paper, the Morse potential is used in the β-part of the collective Bohr Hamiltonian for triaxial nuclei. Energy eigenvalues and eigenfunctions are obtained in a closed form through exactly separating the Hamiltonian into its variables by using an appropriate form of the potential. The results are applied to generate the nuclear spectrum of ¹⁹²Pt, ¹⁹⁴Pt and ¹⁹⁶Pt isotopes which are known to be the best candidate exhibiting triaxiality. Electric quadrupole transition ratios are calculated and then compared with the experimental data and the Z(5) model results.

This paper proposes an improved potential for the $\beta$-part of the collective Bohr Hamiltonian, namely, a Killingbeck plus Morse potential, while the $\gamma$-part is solved for a triaxial deformation close to $\gamma =30^{\circ }$. 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 $B(E2)$ quadrupole transition probabilities of the ${}^{192,194,196}Pt$ isotopes. Moreover, the results of the present solution are compared with those of the well-known $Z(5)$ and $esM$ models.

We present an alternative and accurate solution of the radial Schrödinger equation for the Hellmann potential within the framework of the asymptotic iteration method. We show that the bound state energy eigenvalues can be obtained easily for any n and ℓ values without using any approximations required by other methods. Our results are compared with the findings of other methods.

The spin and pseudo-spin symmetries are analytically investigated by solving the three-dimensional Dirac equation for the Kratzer potential plus a ring-shaped potential. Relativistic Schrödinger-like wave equations coupled in energy are derived from Dirac equation. The energy eigenvalues and eigenfunctions are calculated by solving the coupled relativistic radial, and angular wave equations in the framework of asymptotic iteration method. Our numerical results revealed that the spin and pseudo-spin symmetries are relativistic symmetries of the Dirac Hamiltonian. Effects of the angle-dependent potential on the relativistic energy spectra are also investigated. In addition, we include illustrative tables to examine the solutions in detail.