scholarly journals ASYMPTOTIC ITERATION METHOD FOR SINGULAR POTENTIALS

2008 ◽  
Vol 23 (09) ◽  
pp. 1405-1415 ◽  
Author(s):  
BRODIE CHAMPION ◽  
RICHARD L. HALL ◽  
NASSER SAAD
Keyword(s):  
Wave Function ◽  
Efficient Method ◽  
Iteration Method ◽  
Singular Potential ◽  
Asymptotic Form ◽  
Iteration Process ◽  
Asymptotic Iteration Method ◽  
Singular Potentials ◽  
Radial Schrödinger Equation ◽  
Arbitrary Dimensions

The asymptotic iteration method (AIM) is applied to obtain highly accurate eigenvalues of the radial Schrödinger equation with the singular potential V(r) = r2+λ/rα(α,λ>0) in arbitrary dimensions. Certain fundamental conditions for the application of AIM, such as a suitable asymptotic form for the wave function, and the termination condition for the iteration process, are discussed. Several suggestions are introduced to improve the rate of convergence and to stabilize the computation. AIM offers a simple, accurate, and efficient method for the treatment of singular potentials, such as V(r), valid for all ranges of coupling λ.

Decay rates and masses for some heavy baryons in the hyper-central quark model

2020 ◽  
Vol 35 (10) ◽  
pp. 2050056
Author(s):  
M. Abu-Shady ◽  
M. M. A. Ahmed ◽  
N. H. Gerish
Keyword(s):  
Experimental Data ◽  
Wave Function ◽  
Decay Width ◽  
Iteration Method ◽  
Decay Rates ◽  
Cornell Potential ◽  
Heavy Baryons ◽  
Radial Schrödinger Equation ◽  
Rate Of Decay ◽  
Good Agreement

Masses and decay width for some heavy baryons are studied within Isgur–Wise formalism. The extended Cornell potential is employed. The hyper-radial Schrödinger equation with extended Cornell potential is solved to obtain eigenvalues of energy and baryonic wave function by using the extended iteration method. Masses and the rate of decay width for some heavy baryons are calculated. The present results are improved in comparison with other recent works and are in a good agreement with experimental data.

scholarly journals Relativistic Energy Analysis of Five-Dimensionalq-Deformed Radial Rosen-Morse Potential Combined withq-Deformed Trigonometric Scarf Noncentral Potential Using Asymptotic Iteration Method

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Subur Pramono ◽  
A. Suparmi ◽  
Cari Cari
Keyword(s):  
Wave Function ◽  
Energy Level ◽  
Quantum Number ◽  
Iteration Method ◽  
Morse Potential ◽  
Bound State ◽  
Asymptotic Iteration Method ◽  
Relativistic Energy ◽  
Radial Wave ◽  
Orbital Quantum Number

We study the exact solution of Dirac equation in the hyperspherical coordinate under influence of separableq-deformed quantum potentials. Theq-deformed hyperbolic Rosen-Morse potential is perturbed byq-deformed noncentral trigonometric Scarf potentials, where all of them can be solved by using Asymptotic Iteration Method (AIM). This work is limited to spin symmetry case. The relativistic energy equation and orbital quantum number equationlD-1have been obtained using Asymptotic Iteration Method. The upper radial wave function equations and angular wave function equations are also obtained by using this method. The relativistic energy levels are numerically calculated using Matlab, and the increase of radial quantum numberncauses the increase of bound state relativistic energy level in both dimensionsD=5andD=3. The bound state relativistic energy level decreases with increasing of both deformation parameterqand orbital quantum numbernl.

scholarly journals An alternative solution of diatomic molecules

Open Physics ◽  
2014 ◽  
Vol 12 (2) ◽  
Author(s):  
Özgür Öztemel ◽  
Eser Olğar
Keyword(s):  
Coulomb Potential ◽  
Iteration Method ◽  
Diatomic Molecules ◽  
Alternative Solution ◽  
Asymptotic Iteration Method ◽  
Eigenvalues And Eigenfunctions ◽  
Pseudoharmonic Potential ◽  
Alternative Method ◽  
Radial Schrödinger Equation ◽  
Mie Potential

AbstractThe spectrum of r −1 and r −2 type potentials of diatomic molecules in radial Schrödinger equation are calculated by using the formalism of asymptotic iteration method. The alternative method is used to solve eigenvalues and eigenfunctions of Mie potential, Kratzer-Fues potential, Coulomb potential, and Pseudoharmonic potential by determining the α, β, γ and σ parameters.

EXAMINATION OF $V(r) = -\frac{Z}{r} + gr +\lambda r^2$ POTENTIAL IN THE PRESENCE OF MAGNETIC FIELD

2010 ◽  
Vol 19 (07) ◽  
pp. 1349-1356 ◽  
Author(s):  
M. AYGUN ◽  
Y. SAHIN ◽  
I. BOZTOSUN
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Iteration Method ◽  
Weak Magnetic Field ◽  
Asymptotic Iteration Method ◽  
Two Dimensional ◽  
Strong Magnetic Fields ◽  
Energy Eigenvalues ◽  
Alternative Approach ◽  
Radial Schrödinger Equation

We present an alternative approach, the asymptotic iteration method, to solve the two-dimensional radial Schrödinger equation for [Formula: see text] potential in a magnetic field. The energy eigenvalues for arbitrary Larmor frequencies ranging from ωL = 0.1 to 10.0 are obtained and the results are compared with the nonmagnetic field case, ωL = 0, in order to show the effect of the presence of the weak and strong magnetic fields on the energy eigenvalues. It is shown that the method presented in this paper provides the energy eigenvalues in a systematic way not only in the weak magnetic field but also in the strong magnetic field regions with any Larmor frequencies.

ARBITRARY ℓ-STATE SOLUTION OF THE HELLMANN POTENTIAL

2007 ◽  
Vol 06 (04) ◽  
pp. 893-903 ◽  
Author(s):  
G. KOCAK ◽  
O. BAYRAK ◽  
I. BOZTOSUN
Keyword(s):  
Iteration Method ◽  
State Energy ◽  
Bound State ◽  
Accurate Solution ◽  
State Solution ◽  
Asymptotic Iteration Method ◽  
Bound State Energy ◽  
Energy Eigenvalues ◽  
Radial Schrödinger Equation ◽  
Hellmann Potential

We present an alternative and accurate solution of the radial Schrödinger equation for the Hellmann potential within the framework of the asymptotic iteration method. We show that the bound state energy eigenvalues can be obtained easily for any n and ℓ values without using any approximations required by other methods. Our results are compared with the findings of other methods.

Solusi Persamaan Schrödinger Berbasis Panjang Minimal untuk Potensial Coulomb Termodifikasi

2018 ◽  
Vol 2 (2) ◽  
pp. 43-47
Author(s):  
A. Suparmi, C. Cari, Ina Nurhidayati
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Minimal Length ◽  
Energy Spectra ◽  
Atomic Particle ◽  
Approximate Analytical Solutions ◽  
Radial Schrödinger Equation

Abstrak – Persamaan Schrödinger adalah salah satu topik penelitian yang yang paling sering diteliti dalam mekanika kuantum. Pada jurnal ini persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Fungsi gelombang dan spektrum energi yang dihasilkan menunjukkan kharakteristik atau tingkah laku dari partikel sub atom. Dengan menggunakan metode pendekatan hipergeometri, diperoleh solusi analitis untuk bagian radial persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Hasil yang diperoleh menunjukkan terjadi peningkatan energi yang sebanding dengan meningkatnya parameter panjang minimal dan parameter potensial Coulomb Termodifikasi. Kata kunci: persamaan Schrödinger, panjang minimal, fungsi gelombang, energi, potensial Coulomb Termodifikasi Abstract – The Schrödinger equation is the most popular topic research at quantum mechanics. The  Schrödinger equation based on the concept of minimal length formalism has been obtained for modified Coulomb potential. The wave function and energy spectra were used to describe the characteristic of sub-atomic particle. By using hypergeometry method, we obtained the approximate analytical solutions of the radial Schrödinger equation based on the concept of minimal length formalism for the modified Coulomb potential. The wave function and energy spectra was solved. The result showed that the value of energy increased by the increasing both of minimal length parameter and the potential parameter. Key words: Schrödinger equation, minimal length formalism (MLF), wave function, energy spectra, Modified Coulomb potential

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.

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