Excited states of even-A and odd-A nuclei with deformation-dependent mass parameters for the Kratzer potential

The low-lying collective spectra for axially symmetric nuclei are described within the Bohr–Hamiltonian by considering deformation-dependent mass coefficients and Kratzer potential in [Formula: see text] part. The energy eigenvalues and the total wave function of the problem are obtained in compact forms by means of the asymptotic iteration method. The numerical calculations are carried out for energy spectra as well as electromagnetic transition probabilities, and compared with experimental data in both cases: within and without the deformation-dependent mass (DDM) formalism. We investigate the nuclear observables of four even-A nuclei [Formula: see text]Sm, [Formula: see text]Gd, [Formula: see text]Yb, [Formula: see text]W and two odd-A nuclei [Formula: see text]Yb, [Formula: see text]Dy. Moreover, we will show that the choice of the Kratzer potential minimizes the level spacings within the [Formula: see text] band, which are usually overestimated by Bohr–Hamiltonian with Davidson potential.

Quasinormal Frequencies of a Two-Dimensional Asymptotically Anti-de Sitter Black Hole of the Dilaton Gravity Theory

We numerically calculate the quasinormal frequencies of the Klein-Gordon and Dirac fields propagating in a two-dimensional asymptotically anti-de Sitter black hole of the dilaton gravity theory. For the Klein-Gordon field we use the Horowitz-Hubeny method and the asymptotic iteration method for second order differential equations. For the Dirac field we first exploit the Horowitz-Hubeny method. As a second method, instead of using the asymptotic iteration method for second order differential equations, we propose to take as a basis its formulation for coupled systems of first order differential equations. For the two fields we find that the results that produce the two numerical methods are consistent. Furthermore for both fields we obtain that their quasinormal modes are stable and we compare their quasinormal frequencies to analyze whether their spectra are isospectral. Finally we discuss the main results.

Asymptotic iteration method for solving Hahn difference equations

Hahn’s difference operator $D_{q;w}f(x) =({f(qx+w)-f(x)})/({(q-1)x+w})$ D q ; w f ( x ) = ( f ( q x + w ) − f ( x ) ) / ( ( q − 1 ) x + w ) , $q\in (0,1)$ q ∈ ( 0 , 1 ) , $w>0$ w > 0 , $x\neq w/(1-q)$ x ≠ w / ( 1 − q ) is used to unify the recently established difference and q-asymptotic iteration methods (DAIM, qAIM). The technique is applied to solve the second-order linear Hahn difference equations. The necessary and sufficient conditions for polynomial solutions are derived and examined for the $(q;w)$ ( q ; w ) -hypergeometric equation.

Studying novel 1D potential via the AIM

In this work, we would like to apply the asymptotic iteration method (AIM) to a newly proposed Morse-like deformed potential introduced recently by Assi, Alhaidari and Bahlouli.[Formula: see text] This interesting potential can support bound states and/or resonances. However, in this work, we are only interested in bound states. We considered several choices of the potential parameters and obtained the associated spectrum. Finally, we study the small deformation limit at which this finite spectrum system will transition to infinite spectrum size.

Optimal Perturbation Technique within the Asymptotic Iteration Method for Heavy-Light Meson Mass Splittings

For further insight into the perturbation technique within the framework of the asymptotic iteration method (PAIM), we suggest this method to be used as an alternative method to the traditional well-known perturbation techniques. We show by means of very simple algebraic manipulations that PAIM can be directly applied to obtain the symbolic expectation value of any perturbed potential piece without using the eigenfunction of the unperturbed problem. One of the fundamental advantages of PAIM is its ability to extract a reference unperturbed potential piece or pieces from the total Hamiltonian which can be solved exactly within AIM. After all, one can easily compute the symbolic expectation values of the remaining potential pieces. As an example, the present scheme is applied to the semi-relativistic wave equation with the harmonic-oscillator potential implemented with the Fermi–Breit potential terms. In particular, the non-trivial symbolic expectation values of the Dirac delta function, and the momentum-dependent orbit–orbit coupling terms are successfully calculated. Results are then used, as an illustration, to compute the semi-relativistic s-wave heavy-light meson masses. We obtain good agreement with experimental data for the meson mass splittings cu¯, cd¯, cs¯, bu¯, bd¯, bs¯.

Numerical Solution of Schrodinger Equation for Rotating Morse Potential using Matrix Methods with Fourier Sine Basis

In this paper, an elegant and easy to implement numerical method using matrix mechanics approach is proposed, to solve the time independent Schrodinger equation (TISE) for Morse potential. It is specifically applied to non-homogeneous diatomic molecule HCl to obtain its rotating-vibrator spectrum. While matrix diagonalization technique is utilised for solving TISE, model parameters for Morse potential are optimized using variational Monte-Carlo (VMC) approach by minimizing χ 2 − value. Thus, validation with experimental vibrational frequencies is completely numerical based with no recourse to analytical solutions. The ro-vibrational spectra of HCl molecule obtained using the optimized parameters through VMC have resulted in least χ 2 − value as compared to those determined using best parameters from multiple regression analysis of analytical expressions. Numerical algorithm for solving the Hamiltonian matrix has been implemented utilizing Free Open Source Software (FOSS) Scilab and simulation results are matching well with those obtained using analytical solutions from Nikiforov-Uvarov (NU) method and asymptotic iteration method (AIM).

Closed-form solutions for the Schrödinger wave equation with non-solvable potentials: A perturbation approach

To obtain closed-form solutions for the radial Schrödinger wave equation with non-solvable potential models, we use a simple, easy, and fast perturbation technique within the framework of the asymptotic iteration method (PAIM). We will show how the PAIM can be applied directly to find the analytical coefficients in the perturbation series, without using the base eigenfunctions of the unperturbed problem. As an example, the vector Coulomb ( ∼ 1 / r ) \left( \sim 1\hspace{0.1em}\text{/}\hspace{0.1em}r) and the harmonic oscillator ( ∼ r 2 ) \left( \sim {r}^{2}) plus linear ( ∼ r ) \left( \sim r) scalar potential parts implemented with their counterpart spin-dependent terms are chosen to investigate the meson sectors including charm and beauty quarks. This approach is applicable in the same form to both the ground state and the excited bound states and can be easily applied to other strongly non-solvable potential problems. The procedure of this method and its results will provide a valuable hint for investigating tetraquark configuration.

Numerical Solution of Schrodinger Equation for Morse Potential using Matrix Methods with Fourier Sine Basis

In this paper, an elegant and easy to implement numerical method using matrix mechanics approach is proposed, to solve the time independent Schrodinger equation (TISE) for Morse potential. It is specifically applied to non-homogeneous diatomic molecule HCl to obtain its rotating-vibrator spectrum. While matrix diagonalization technique is utilised for solving TISE, model parameters for Morse potential are optimized using variational Monte-Carlo (VMC) approach by minimizing $\chi^2-$ value. Thus, validation with experimental vibrational frequencies is completely numerical based with no recourse to analytical solutions. The ro-vibrational spectra of HCl molecule obtained using the optimized parameters through VMC have resulted in least $\chi^2-$ value as compared to those determined using best parameters from multiple regression analysis of analytical expressions. Numerical algorithm for solving the Hamiltonian matrix has been implemented utilizing Free Open Source Software (FOSS) Scilab and simulation results are matching well with those obtained using analytical solutions from Nikiforov-Uvarov (NU) method and asymptotic iteration method (AIM).

Bound state solutions of the Klein–Gordon equation with energy-dependent potentials

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.