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 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.

scholarly journals Relativistic study of the energy-dependent Coulomb potential including Coulomb-like tensor interaction

2012 ◽  
Vol 90 (7) ◽  
pp. 655-660 ◽  
Author(s):  
M. Hamzavi ◽  
S.M. Ikhdair
Keyword(s):  
Dirac Equation ◽  
Quantum Number ◽  
Coulomb Potential ◽  
Iteration Method ◽  
Arbitrary Spin ◽  
Tensor Interaction ◽  
Asymptotic Iteration Method ◽  
Spin Orbit ◽  
Energy Eigenvalues ◽  
Energy Dependent

The exact Dirac equation for the energy-dependent Coulomb (EDC) potential including a Coulomb-like tensor (CLT) potential has been studied in the presence of spin and pseudospin symmetries with arbitrary spin–orbit quantum number, κ. The energy eigenvalues and corresponding eigenfunctions are obtained in the framework of the asymptotic iteration method. Some numerical results are obtained in the presence and absence of EDC and CLT potentials.

Nonrelativistic and relativistic bound state solutions of the molecular Tietz potential via the improved asymptotic iteration method

2014 ◽  
Vol 92 (3) ◽  
pp. 215-220 ◽  
Author(s):  
W.A. Yahya ◽  
K. Issa ◽  
B.J. Falaye ◽  
K.J. Oyewumi
Keyword(s):  
Iteration Method ◽  
Vibrational Energy ◽  
Bound State ◽  
Asymptotic Iteration Method ◽  
Quantum Numbers ◽  
Approximate Analytical Solutions ◽  
Relative Closeness ◽  
Klein Gordon ◽  
Tietz Potential ◽  
Schrödinger System

We have obtained the approximate analytical solutions of the relativistic and nonrelativistic molecular Tietz potential using the improved asymptotic iteration method. By approximating the centrifugal term through the Greene–Aldrich approximation scheme, we have obtained the energy eigenvalues and wave functions for all orbital quantum numbers [Formula: see text]. Where necessary, we made comparison with the result obtained previously in the literature. The relative closeness of the two results reveal the accuracy of the method presented in this study. We proceed further to obtain the rotational-vibrational energy spectrum for some diatomic molecules. These molecules are CO, HCl, H2, and LiH. We have also obtained the relativistic bound state solution of the Klein−Gordon equation with this potential. In the nonrelativistic limits, our result converges to that of the Schrödinger system.

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.

ON ASYMPTOTICS OF THREE-BODY BOUND STATE RADIAL WAVE FUNCTIONS OF HALO NUCLEI NEAR THE HYPERANGLE φ~0 AND φ~π/2 IN THE CONFIGURATION SPACE AND THREE-BODY ASYMPTOTIC NORMALIZATION FACTORS FOR 6He NUCLEUS IN THE (n+n+α)-CHANNEL

2009 ◽  
Vol 18 (07) ◽  
pp. 1561-1585 ◽  
Author(s):  
R. YARMUKHAMEDOV ◽  
M. K. UBAYDULLAEVA
Keyword(s):  
Wave Function ◽  
Configuration Space ◽  
Bound State ◽  
Wave Functions ◽  
Halo Nuclei ◽  
Asymptotic Normalization ◽  
Radial Wave ◽  
Asymptotic Expressions ◽  
Three Body ◽  
Normalization Factors

Asymptotic expressions for the bound state radial partial wave functions of three-body (nnc) halo nuclei with two loosely bound valence neutrons (n) are obtained in explicit form, when the relative distance between two neutrons (r) tends to infinity and the relative distance between the center of mass of core (c) and two neutrons (ρ) is too small or vice versa. These asymptotic expressions contain a factor that can strongly influence the asymptotic values of the three-body radial wave function in the vicinity of the hyperangle of φ~0 except 0 (r→∞ and ρ is too small except 0) or φ~π/2 except π/2 (ρ→∞ and r is too small except 0) in the configuration space. The derived asymptotic forms are applied to the analysis of the asymptotic behavior of the three-body (nnα) wave function for 6He nucleus obtained by other authors on the basis of multicluster stochastic variational method using the two forms of the αN-potential. The ranges of r (or ρ) from the asymptotical regions are determined for which the agreement between the calculated wave function and the asymptotics formulae is reached. Information about the values of the three-body asymptotic normalization factors is extracted.

scholarly journals Возбуждение и ионизация частицы в одномерной потенциальной яме нулевого радиуса предельно коротким световым импульсом

2022 ◽  
Vol 130 (3) ◽  
pp. 414
Author(s):  
Р.М. Архипов ◽  
М.В. Архипов ◽  
А.В. Пахомов ◽  
Н.Н. Розанов
Keyword(s):  
Wave Function ◽  
Energy Level ◽  
Short Pulse ◽  
Bound State ◽  
Characteristic Scale ◽  
Potential Well ◽  
One Dimensional ◽  
Characteristic Period ◽  
Zero Radius ◽  
Perturbation Approximation

The Migdal sudden perturbation approximation is used to solve the problem of excitation and ionization particles in a one-dimensional potential of zero radius with an extremely short pulse. There is has only one energy level in such a one-dimensional the delta-shaped potential well. It is shown that for pulse durations shorter than the characteristic period of oscillations of the wave function of the particle in the bound state, the population of the level (and the probability of ionization) is determined by the ratio of the electric the area of ​​the pulse to the characteristic “scale” of the area inversely proportional to the area of ​​localization of the particle in a bound state.

scholarly journals Bound state solutions of the Schrödinger equation with energy-dependent molecular Kratzer potential via asymptotic iteration method

2020 ◽  
Vol 45 (1) ◽  
pp. 65 ◽  
Author(s):  
Akpan Ndem Ikot ◽  
Uduakobong Okorie ◽  
Alalibo Thompson Ngiagian ◽  
Clement Atachegbe Onate ◽  
Collins Okon Edet ◽  
...  
Keyword(s):  
Schrödinger Equation ◽  
Iteration Method ◽  
Schrodinger Equation ◽  
Graphical Representation ◽  
Bound State ◽  
Confluent Hypergeometric Function ◽  
Asymptotic Iteration Method ◽  
Slope Parameter ◽  
Exact Bound ◽  
Energy Dependent

In this paper, we obtained the exact bound state energy spectrum of the Schrödinger equation with energy dependent molecular Kratzer potential using asymptotic iteration method (AIM). The corresponding wave function expressed in terms of the confluent hypergeometric function was also obtained. As a special case, when the energy slope parameter in the energy-dependent molecular Kratzer potential is set to zero, then the well-known molecular Kratzer potential is recovered. Numerical results for the energy eigenvlaues are also obtained for different quantum states, in the presence and absence of the energy slope parameter. These results are discussed extensively using graphical representation. Our results are seen to agree with the results in literature.

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