Eser Olgar

The exact solution of the s-wave Klein–Gordon equation for the generalized Hulthén potential by the asymptotic iteration method

The bound state solution of the (1+1)-dimensional Klein?Gordon (KG) equation for the generalized Hulth?n potential has been studied in the framework of the asymptotic iteration method (AIM). The energy values and the corresponding eigenfunctions are obtained for mixed forms of the Hulth?n vector potential and scalar potential.

Bound States of the S-Wave Equation with Equal Scalar and Vector Standard Eckart Potential

A supersymmetric technique for the bound-state solutions of the s-wave Klein–Gordon equation with equal scalar and vector standard Eckart-type potential is proposed. Its exact solutions are obtained. Possible generalization of our approach is outlined.

An Alternative Method for Calculating Bound-State of Energy Eigenvalues of Klein?Gordon for Quasi-exactly Solvable Potentials

We obtain the bound-state energy of the Klein–Gordon equation for some examples of quasi-exactly solvable potentials within the framework of asymptotic iteration method (AIM). The eigenvalues are calculated for type-1 solutions. The whole quasi-exactly solvable potentials are generated from the defined relation between the vector and scalar potentials.

Solution of a Hamiltonian of quantum dots with Rashba spin–orbit coupling: quasi-exact solution

We present a method to solve the problem of Rashba spin–orbit coupling in semiconductor quantum dots, within the context of quasi-exactly solvable spectral problems. We show that the problem possesses a hidden osp(2, 2) superalgebra. We constructed a general matrix whose determinant provides exact eigenvalues. Analogous mathematical structures between the Rashba and some of the other spin-boson physical systems are noted.

Exact Solution of Klein–Gordon Equation by Asymptotic Iteration Method

Using the asymptotic iteration method (AIM) we obtain the spectrum of the Klein–Gordon equation for some choices of scalar and vector potentials. In particular, it is shown that the AIM exactly reproduces the spectrum of some solvable potentials.

Asymptotic Iteration Method for Energies of Inversely Linear Potential with Spatially Dependent Mass

The bound-state solution of the position dependent mass Klein–Gordon equation including inversely linear potential is obtained within the framework of the asymptotic iteration method. The relation between the scalar and vector potentials is considered to S(x) = V(x)(β − 1). In particular, it is shown that the corresponding method exactly reproduces the spectrum of linearly inversely potentials with spatially dependent mass.

Algebraic treatments of the problems of the spin-1/2 particles in the one- and two-dimensional geometry: A systematic study

Abstract We consider solutions of the 2xa0×xa02 matrix Hamiltonians of the physical systems within the context of the suxa0(2) and suxa0(1,xa01) Lie algebras. Our technique is relatively simple when compared with those of others and treats those Hamiltonians which can be treated in a unified framework of the Spxa0(4,xa0R) algebra. The systematic study presented here reproduces a number of earlier results in a natural way as well as leads to a novel finding. Possible generalizations of the method are also suggested.

Bound-State Solution of s-Wave Klein-Gordon Equation for Woods-Saxon Potential

The bound-state solution of s-wave Klein-Gordon equation is calculated for Woods-Saxon potential by using the asymptotic iteration method (AIM). The energy eigenvalues and eigenfunctions are obtained for the required condition of bound-state solutions.

An alternative solution of diatomic molecules

A strong structural regularity of classes is found in soccer teams ranked by the Union of European Football Associations (UEFA) for the time interval 2009-2014. It concerns 424 to 453 teams according to the 5 competition seasons. The analysis is based on the rank-size theory considerations, the size being the UEFA coefficient at the end of a season. Three classes emerge: (i) the few top teams, (ii) 300 teams, (iii) the rest of the involved teams (about 150) in the tail of the distribution. There are marked empirical laws describing each class. A 3-parameter Lavalette function is used to describe the concave curving as the rank increases, and to distinguish the the tail from the central behavior.The 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.

A Novel Approach to Solve Quasiexactly Solvable Pauli Equation

The spectra for some specific forms of external magnetic fields in Pauli equation are obtained in the framework of the asymptotic iteration method (AIM). AIM is applied to find the solution of Pauli equation. When the method is applied to quasiexactly solvable systems, it not only easily gives the corresponding spectrum, but also produces accurate results for the eigenvalues of the system having sl(2) symmetry.