scholarly journals Large-order shifted 1/Nexpansions through the asymptotic iteration method

2007 ◽  
Vol 41 (1) ◽  
pp. 015301 ◽  
Author(s):  
T Barakat
Keyword(s):  
Iteration Method ◽  
Asymptotic Iteration Method ◽  
Large Order

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.

THE ASYMPTOTIC ITERATION METHOD FOR DIRAC AND KLEIN–GORDON EQUATIONS WITH A LINEAR SCALAR POTENTIAL

2006 ◽  
Vol 21 (19n20) ◽  
pp. 4127-4135 ◽  
Author(s):  
T. BARAKAT
Keyword(s):  
Iteration Method ◽  
Bound States ◽  
Scalar Potential ◽  
Asymptotic Iteration Method ◽  
Klein Gordon ◽  
Linear Scalar

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.

scholarly journals Asymptotic iteration method solutions to the relativistic Duffin-Kemmer-Petiau equation

2006 ◽  
Vol 47 (6) ◽  
pp. 062301 ◽  
Author(s):  
I. Boztosun ◽  
M. Karakoc ◽  
F. Yasuk ◽  
A. Durmus
Keyword(s):  
Iteration Method ◽  
Asymptotic Iteration Method

scholarly journals The asymptotic iteration method for the angular spheroidal eigenvalues with arbitrary complex size parameter c

2006 ◽  
Vol 84 (2) ◽  
pp. 121-129 ◽  
Author(s):  
T Barakat ◽  
K Abodayeh ◽  
B Abdallah ◽  
O M Al-Dossary
Keyword(s):  
Excellent Agreement ◽  
Iteration Method ◽  
Full Range ◽  
Numerical Results ◽  
Asymptotic Iteration Method ◽  
Published Data ◽  
Size Parameter ◽  
Arbitrary Complex ◽  
Parameter Values

The asymptotic iteration method is applied to calculate the angular spheroidal eigenvalues [Formula: see text] (c) with arbitrary complex size parameter c. It is shown that the numerical results obtained for [Formula: see text] (c) are all in excellent agreement with the available published data over the full range of parameter values [Formula: see text] m, and c. Some representative values of [Formula: see text] (c) for large real c are also given.PACS No.: 02.70.–c.

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