Ramazan Sever

A GENERAL APPROACH FOR THE EXACT SOLUTION OF THE SCHRODINGER EQUATION

Abstract Effective mass Schrödinger equation is solved exactly for a given potential. Nikiforov-Uvarov method is used to obtain energy eigenvalues and the corresponding wave functions. A free parameter is used in the transformation of the wave function. The effective mass Schrödinger equation is also solved for the Morse potential transforming to the constant mass Schrödinger equation for a potential. One can also get solution of the effective mass Schrödinger equation starting from the constant mass Schrödinger equation.

Approximate bound state solutions of Dirac equation with Hulthén potential including Coulomb-like tensor potential

We solve the Dirac equation approximately for the attractive scalar S(r) and repulsive vector V(r) Hulthen potentials including a Coulomb-like tensor potential with arbitrary spin-orbit coupling quantum number @k. In the framework of the spin and pseudospin symmetric concept, we obtain the analytic energy spectrum and the corresponding two-component upper- and lower-spinors of the two Dirac particles by means of the Nikiforov-Uvarov method in closed form. The limit of zero tensor coupling and the non-relativistic solution are obtained. The energy spectrum for various levels is presented for several @k values under the condition of exact spin symmetry in the presence or absence of tensor coupling.

Polynomial solutions of the Schrödinger equation for the generalized Woods-Saxon potential

The bound state energy eigenvalues and the corresponding eigenfunctions of the generalized Woods Saxon potential are obtained in terms of the Jacobi polynomials. Nikiforov-Uvarov method is used in the calculations. It is shown that the results are in a good agreement with the ones obtained before.

Any l-state improved quasi-exact analytical solutions of the spatially dependent mass Klein–Gordon equation for the scalar and vector Hulthén potentials

We present a new approximation scheme for the centrifugal term to obtain a quasi-exact analytical bound state solution within the framework of the position-dependent effective mass radial Klein?Gordon equation with the scalar and vector Hulth?n potentials in any arbitrary D dimension and orbital angular momentum quantum numbers l. The Nikiforov?Uvarov (NU) method is used in the calculations. The relativistic real energy levels and corresponding eigenfunctions for the bound states with different screening parameters have been given in a closed form. It is found that the solutions in the case of constant mass and in the case of s-wave (l=0) are identical with the ones obtained in the literature.

Exact Solutions Of The Modified Kratzer Potential Plus Ring-Shaped Potential In The D-Dimensional Schrödinger Equation By The Nikiforov–Uvarov Method

We present analytically the exact energy bound-states solutions of the Schrodinger equation in D dimensions for a recently proposed modified Kratzer plus ring-shaped potential by means of the Nikiforov–Uvarov method. We obtain an explicit solution of the wave functions in terms of hyper-geometric functions (Laguerre polynomials). The results obtained in this work are more general and true for any dimension which can be reduced to the well-known three-dimensional forms given by other works.

Bound states of the Dirac equation for the PT-symmetric generalized Hulthen potential by the Nikiforov-Uvarov method

Abstract The one-dimensional Dirac equation is solved for the PT -symmetric generalized Hulthen potential. The Nikiforov–Uvarov method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type is used to obtain exact energy eigenvalues and corresponding eigenfunctions.

Exact Solution of the Klein-Gordon Equation for the PT -Symmetric Generalized Woods-Saxon Potential by the Nikiforov-Uvarov Method

The one-dimensional Klein-Gordon (KG) equation has been solved for the PT -symmetric generalized Woods-Saxon (WS) potential. The NikiforovUvarov (NU) method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type is used to obtain exact energy eigenvalues and corresponding eigenfunctions. We have also investigated the positive and negative exact bound states of the s-states for different types of complex generalized WS potentials.

APPROXIMATE ANALYTICAL SOLUTIONS OF THE KLEIN-GORDON EQUATION FOR THE HULTHEN POTENTIAL WITH THE POSITION-DEPENDENT MASS

The Klein–Gordon equation is solved approximately for the Hulthen potential for any angular momentum quantum number l with the position-dependent mass. Solutions are obtained by reducing the Klein–Gordon equation into a Schrodinger-like differential equation using an appropriate coordinate transformation. The Nikiforov–Uvarov method is used in the calculations to get energy eigenvalues and the wavefunctions. It is found that the results in the case of constant mass are in good agreement with the ones obtained in the literature.

A PERTURBATIVE TREATMENT FOR THE ENERGY LEVELS OF NEUTRAL ATOMS

Energy levels of neutral atoms have been reexamined by applying an alternative perturbative scheme in solving the Schrodinger equation for the Yukawa potential model with a modified screening parameter. The predicted shell binding energies are found to be quite accurate over the entire range of the atomic number Z up to 84 and compare very well with those obtained within the framework of hypervirial-Pade scheme and the method of shifted large-N expansion. It is observed that the new perturbative method may also be applied to the other areas of atomic physics.

TWO APPROXIMATION SCHEMES TO THE BOUND STATES OF THE DIRAC-HULTHEN PROBLEM

The bound-state (energy spectrum and two-spinor wavefunctions) solutions of the Dirac equation with the Hulthen potential for all angular momenta based on the spin and pseudospin symmetry are obtained. The parametric generalization of the Nikiforov–Uvarov method is used in the calculations. The orbital dependence (spin–orbit- and pseudospin–orbit-dependent coupling too singular 1/r2) of the Dirac equation are included to the solution by introducing a more accurate approximation scheme to deal with the centrifugal (pseudo-centrifugal) term. The approximation is also made for the less singular 1/r orbital term in the Dirac equation for a wider energy spectrum. The nonrelativistic limits are also obtained on mapping of parameters.