The asymptotic iteration method for the eigenenergies of the anharmonic oscillator potential

2005 ◽  
Vol 344 (6) ◽  
pp. 411-417 ◽  
Author(s):  
T. Barakat
Keyword(s):  
Iteration Method ◽  
Anharmonic Oscillator ◽  
Asymptotic Iteration Method ◽  
Oscillator Potential ◽  
Anharmonic Oscillator Potential

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.

THE ASYMPTOTIC ITERATION METHOD FOR THE EIGENENERGIES OF THE ASYMMETRICAL QUANTUM ANHARMONIC OSCILLATOR POTENTIALS $V(x)=\sum_{j=2}^{2\alpha}A_{j}x^{j}$

2007 ◽  
Vol 22 (01) ◽  
pp. 203-212 ◽  
Author(s):  
T. BARAKAT ◽  
O. M. AL-DOSSARY
Keyword(s):  
Rate Of Convergence ◽  
Iteration Method ◽  
Anharmonic Oscillator ◽  
Full Range ◽  
Adjustable Parameter ◽  
Numerical Results ◽  
Asymptotic Iteration Method ◽  
Anharmonic Oscillators ◽  
Parameter Values

The asymptotic iteration method is used to calculate the eigenenergies for the asymmetrical quantum anharmonic oscillator potentials [Formula: see text], 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 Aj.

Bound state solution of the Dirac equation for a new anharmonic oscillator potential

2007 ◽  
Vol 76 (5) ◽  
pp. 442-444 ◽  
Author(s):  
Gao-Feng Wei ◽  
Chao-Yun Long ◽  
Zhi He ◽  
Shui-Jie Qin ◽  
Jing Zhao
Keyword(s):  
Dirac Equation ◽  
Anharmonic Oscillator ◽  
Bound State ◽  
State Solution ◽  
Bound State Solution ◽  
Oscillator Potential ◽  
Anharmonic Oscillator Potential

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.

scholarly journals Bohr Hamiltonian with a potential having spherical and deformed minima at the same depth

2018 ◽  
Vol 194 ◽  
pp. 01007
Author(s):  
Petrica Buganu ◽  
Radu Budaca ◽  
Andreea-Ioana Budaca
Keyword(s):  
Critical Point ◽  
Bessel Functions ◽  
Anharmonic Oscillator ◽  
Transition Probabilities ◽  
Local Maximum ◽  
Numerical Data ◽  
Energy Spectra ◽  
Oscillator Potential ◽  
Good Tool ◽  
Anharmonic Oscillator Potential

A solution for the Bohr-Mottelson Hamiltonian with an anharmonic oscillator potential of sixth order, obtained through a diagonalization in a basis of Bessel functions, is presented. The potential is consid- ered to have simultaneously spherical and deformed minima of the same depth separated by a barrier (a local maximum). This particular choice is appropriate to describe the critical point of the nuclear phase transition from a spherical vibrator to an axial rotor. Up to a scale factor, which can be cancelled by a corresponding normalization, the energy spectra and the electromagnetic E2 transition probabilities depend only on a single free parameter related to the height of the barrier. Investigations of the numerical data revealed that the model represents a good tool to describe this critical point.

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