Cevdet Tezcan

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 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.

Approximate Analytical Solutions of the Klein-Gordon Equation for Hulthen Potential with 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.

Exact Solutions Of The Dirac Equation With Harmonic Oscillator Potential Including A Coulomb-Like Tensor Potential

In this work, we study the Dirac equation with scalar, vector, and tensor interactions. The Dirac Hamiltonian contains quadratic scalar and vector potentials, as well as a tensor potential. The tensor potential is taken as a sum of a linear term and a Coulomb-like term. It is shown that the tensor potential preserves the form of the harmonic oscillator potential and generates spin-orbit terms. The energy eigenvalues and the corresponding eigenfunctions are obtained for different alternatives.

The HN method for solving linear transport equation: theory and applications

Abstract The system of singular integral equations which is obtained from the integro-differential form of the linear transport equation using the Placzek lemma is solved. The exit distributions at the boundaries of the various media and the infinite medium Greens function are used. The process is applied to the half-space and finite slab problems. The neutron angular density in terms of singular eigenfunctions of the method of elementary solutions is also used to derive the same analytical expressions.

A fictitious slab with vanishing critical thickness

Abstract In one-speed neutron transport theory, it is shown that a fictitious anisotropic fission and scattering kernel with an extreme forward bias would give a critical slab thickness varying non-monotonically with anisotropy. For this particular kernel, the critical thickness increases first with increasing forward bias but decreases later and vanishes at a pertain critical anisotropy. This is a geometrical effect which may be understood by considering the variation of the angular distribution with effectively increasing multiplicity.

The critical slab with the backward-forward-isotropic scattering model

Abstract The variation of the critical slab thickness from backward to forward scattering is studied for specified isotropic scattering. Numerical results are obtained from the zeroth and first-order approximate analytical expressions, derived using the method of elementary solutions. It is shown that the critical slab thickness increases monotonically with increasing forward anisotropy.

EXACT SOLUTION OF THE SCHRÖDINGER EQUATION FOR THE MODIFIED KRATZER'S MOLECULAR POTENTIAL WITH POSITION-DEPENDENT MASS

Exact solutions of Schrodinger equation are obtained for the modified Kratzer and the corrected Morse potentials with the position-dependent effective mass. The bound state energy eigenvalues and the corresponding eigenfunctions are calculated for any angular momentum for target potentials. Various forms of point canonical transformations are applied.

The criticality problems with the FN method for the FBIS model

Abstract In one-speed, time-independent, neutron transport theory, the F N method is used for the FBIS (forward-backward-isotropic scattering) model to reinvestigate the behaviour of the critical size in plane and spherical geometries. For the FIS (forward-isotropic scattering) model the numerical results are compared with previously obtained variational results and it is shown that they are in agreement. For the BIS (backward-isotropic scattering) model exact results are obtained and compared with the first-order approximate results obtained using the method of elementary solutions.

The FN method for anisotropic scattering in neutron transport theory: The half-space problems

Abstract The FN method is extended for problems for extremely anisotropic scattering and applied to the half-space albedo and the constant source problems.