scholarly journals Study of the Generalized Quantum Isotonic Nonlinear Oscillator Potential

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
Nasser Saad ◽  
Richard L. Hall ◽  
Hakan Çiftçi ◽  
Özlem Yeşiltaş
Keyword(s):  
Iteration Method ◽  
Nonlinear Oscillator ◽  
High Accuracy ◽  
Asymptotic Iteration Method ◽  
Oscillator Potential ◽  
Quasipolynomial Solutions ◽  
Potential Parameters ◽  
Explicit Expressions

We study the generalized quantum isotonic oscillator Hamiltonian given byH=−d2/dr2+l(l+1)/r2+w2r2+2g(r2−a2)/(r2+a2)2,g>0. Two approaches are explored. A method for finding the quasipolynomial solutions is presented, and explicit expressions for these polynomials are given, along with the conditions on the potential parameters. By using the asymptotic iteration method, we show how the eigenvalues of this Hamiltonian for arbitrary values of the parametersg,w, andamay be found to high accuracy.

SOLUTION FOR THE EIGENENERGIES OF SEXTIC ANHARMONIC OSCILLATOR POTENTIAL V(x)=A6x6+A4x4+A2x2

2006 ◽  
Vol 21 (21) ◽  
pp. 1675-1682 ◽  
Author(s):  
A. J. SOUS
Keyword(s):  
Excited States ◽  
Iteration Method ◽  
Anharmonic Oscillator ◽  
High Accuracy ◽  
Asymptotic Iteration Method ◽  
Oscillator Potential ◽  
Anharmonic Oscillator Potential

In this paper a study of the sextic anharmonic oscillator potential V(x)=A6x6+A4x4+A2x2 (A6≠0) using the asymptotic iteration method is presented. We calculate the eigenenergies for different excited states. The used method works very well for this potential and in fact one is able to obtain high accuracy with the asymptotic iteration method. A comparison between our results with other methods found in literature is presented.

Studying novel 1D potential via the AIM

2021 ◽  
pp. 2150141
Author(s):  
A. J. Sous
Keyword(s):  
Iteration Method ◽  
Bound States ◽  
Small Deformation ◽  
Asymptotic Iteration Method ◽  
Finite Spectrum ◽  
Deformation Limit ◽  
Potential Parameters

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.

Application of asymptotic iteration method to the Khare-Mandal and its PT-symmetric QES partner potential

Open Physics ◽  
2008 ◽  
Vol 6 (4) ◽  
Author(s):  
Okan Özer ◽  
Vedat Aslan
Keyword(s):  
Iteration Method ◽  
Asymptotic Iteration Method ◽  
Complex Conjugate ◽  
Eigenvalues And Eigenfunctions ◽  
Energy Eigenvalues ◽  
Exactly Solvable ◽  
Potential Parameters ◽  
Partner Potential

AbstractWe study the application of the asymptotic iteration method to the Khare-Mandal potential and its PT-symmetric partner. The eigenvalues and eigenfunctions for both potentials are obtained analytically. We have shown that although the quasi-exactly solvable energy eigenvalues of the Khare-Mandal potential are found to be in complex conjugate pairs for certain values of potential parameters, its PT-symmetric partner exhibits real energy eigenvalues in all cases.

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.

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