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.

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 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.

A new class of Pöschl–Teller potentials with inverse square singularity and their spectra using the asymptotic iteration method

2018 ◽  
Vol 33 (22) ◽  
pp. 1850128 ◽  
Author(s):  
I. A. Assi ◽  
A. J. Sous ◽  
H. Bahlouli
Keyword(s):  
Iteration Method ◽  
Bound States ◽  
Jacobi Polynomials ◽  
Basis Set ◽  
Approximation Schemes ◽  
Asymptotic Iteration Method ◽  
S Wave ◽  
New Class ◽  
New Family ◽  
The Matrix

The aim of this work is to introduce a new family of potentials with inverse square singularity which we called the Pöschl–Teller family of potentials. We enforced the matrix representation of the wave operator to be symmetric and (2k[Formula: see text]+[Formula: see text]1) band-diagonal with respect to a square integrable basis set. This, in principle, is only satisfied for specific potential functions within the used basis set. The basis functions we used here are written in terms of Jacobi polynomials, which is the same basis used in the Tridiagonal Representation Approach (TRA). This yield a more general form of Pöschl–Teller potential that can have many terms which could be beneficial for modeling different physical systems where this potential applies. As an illustration, we have studied a specific new five-parameter potential that belongs to this new family and calculated the bound states for both s-wave and l-wave cases using the Asymptotic Iteration Method (AIM). Along the way, we have introduced new approximation schemes to deal with the l-wave centrifugal potential within the AIM at different approximation orders.

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 Bound states of a Klein–Gordon particle in the presence of a smooth potential well

2020 ◽  
Vol 35 (23) ◽  
pp. 2050140
Author(s):  
Eduardo López ◽  
Clara Rojas
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
Bound State ◽  
Potential Well ◽  
One Dimensional ◽  
Smooth Potential ◽  
Klein Gordon ◽  
The One ◽  
Potential Parameters ◽  
Klein Gordon Equation

We solve the one-dimensional time-independent Klein–Gordon equation in the presence of a smooth potential well. The bound state solutions are given in terms of the Whittaker [Formula: see text] function, and the antiparticle bound state is discussed in terms of potential parameters.

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.

Analytical solution of the Shredinger equation for the linear combination of the Manning-Rosen and the class of Yukawa potential

2021 ◽  
pp. 157-169
Author(s):  
G.A. Bayramova ◽  
Keyword(s):  
Analytical Solution ◽  
Bound States ◽  
Hypergeometric Functions ◽  
Yukawa Potential ◽  
Energy Levels ◽  
Energy Eigenvalue ◽  
Radial Wave ◽  
Rosen Potential ◽  
Analytical Expressions ◽  
Potential Parameters

In the present work, an analytical solution for bound states of the modified Schrödinger equation is found for the new supposed combined Manning-Rosen potential plus the Yukawa class. To overcome the difficulties arising in the case l ≠ 0 in the centrifugal part of the Manning-Rosen potential plus the Yukawa class for bound states, we applied the developed approximation. Analytical expressions for the energy eigenvalue and the corresponding radial wave functions for an arbitrary value l ≠ 0 of the orbital quantum number are obtained. And also obtained eigenfunctions expressed in terms of hypergeometric functions. It is shown that energy levels and eigenfunctions are very sensitive to the choice of potential parameters.

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