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

Universe ◽  
2021 ◽  
Vol 7 (6) ◽  
pp. 180
Author(s):  
Haifa I. Alrebdi ◽  
Thabit Barakat
Keyword(s):  
Iteration Method ◽  
Perturbation Technique ◽  
Light Meson ◽  
Asymptotic Iteration Method ◽  
Meson Mass ◽  
Relativistic Wave Equation ◽  
Expectation Values ◽  
Optimal Perturbation ◽  
Dirac Delta ◽  
Unperturbed Problem

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¯.

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

Open Physics ◽  
2021 ◽  
Vol 19 (1) ◽  
pp. 208-214
Author(s):  
Haifa Ibrahim Alrebdi ◽  
Thabit Barakat
Keyword(s):  
Wave Equation ◽  
Closed Form ◽  
Bound States ◽  
Perturbation Technique ◽  
Scalar Potential ◽  
Asymptotic Iteration Method ◽  
Perturbation Approach ◽  
Closed Form Solutions ◽  
Solvable Potential ◽  
Unperturbed Problem

Abstract 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.

scholarly journals THE ENERGY EIGENVALUES OF THE TWO DIMENSIONAL HYDROGEN ATOM IN A MAGNETIC FIELD

2006 ◽  
Vol 15 (06) ◽  
pp. 1263-1271 ◽  
Author(s):  
A. SOYLU ◽  
O. BAYRAK ◽  
I. BOZTOSUN
Keyword(s):  
Magnetic Field ◽  
Hydrogen Atom ◽  
Iteration Method ◽  
Weak Magnetic Field ◽  
The Other ◽  
Asymptotic Iteration Method ◽  
Iterative Approach ◽  
Two Dimensional ◽  
Energy Eigenvalues ◽  
The Magnetic Field

In this paper, the energy eigenvalues of the two dimensional hydrogen atom are presented for the arbitrary Larmor frequencies by using the asymptotic iteration method. We first show the energy eigenvalues for the case with no magnetic field analytically, and then we obtain the energy eigenvalues for the strong and weak magnetic field cases within an iterative approach for n=2-10 and m=0-1 states for several different arbitrary Larmor frequencies. The effect of the magnetic field on the energy eigenvalues is determined precisely. The results are in excellent agreement with the findings of the other methods and our method works for the cases where the others fail.

EIGENENERGIES FOR THE RAZAVY POTENTIAL V(x) = (ζ cosh 2x-M)2 USING THE ASYMPTOTIC ITERATION METHOD

2007 ◽  
Vol 22 (22) ◽  
pp. 1677-1684 ◽  
Author(s):  
A. J. SOUS
Keyword(s):  
Excited States ◽  
Iteration Method ◽  
Asymptotic Iteration Method ◽  
Arbitrary Parameter ◽  
Exactly Solvable

By using the asymptotic iteration method, we have calculated numerically the eigenenergies En 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.

scholarly journals Asymptotic iteration method for solving Hahn difference equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Lucas MacQuarrie ◽  
Nasser Saad ◽  
Md. Shafiqul Islam
Keyword(s):  
Difference Equations ◽  
Iteration Method ◽  
Difference Operator ◽  
Sufficient Conditions ◽  
Asymptotic Iteration Method ◽  
Order Linear ◽  
Polynomial Solutions ◽  
Hahn Difference Equations ◽  
Iteration Methods ◽  
Necessary And Sufficient

AbstractHahn’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.

scholarly journals Solution of Five-dimensional Schrodinger equation for Kratzer’s potential and trigonometric tangent squared potential with asymptotic iteration method (AIM)

2017 ◽  
Vol 1 (2) ◽  
pp. 115
Author(s):  
Agung Budi Prakoso ◽  
A Suparmi ◽  
C Cari
Keyword(s):  
Quantum Number ◽  
Iteration Method ◽  
Diatomic Molecules ◽  
Dimensional Space ◽  
Numerical Data ◽  
Asymptotic Iteration Method ◽  
Radial Part ◽  
Dimensional Solution ◽  
Angular Part ◽  
Kratzer’S Potential

Non-relativistic bound-energy of diatomic molecules determined by non-central potentials in five dimensional solution using AIM. Potential in five dimensional space consist of Kratzer’s potential for radial part and Tangent squared potential for angular part. By varying <em>n<sub>r</sub></em>, <em>n</em><sub>1</sub>, <em>n</em><sub>2</sub>, <em>n</em><sub>3</sub>, dan <em>n</em><sub>4</sub> quantum number on CO, NO, dan I<sub>2</sub> diatomic molecules affect bounding energy values. It knows from its numerical data.

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