Spin and pseudospin symmetry along with orbital dependency of the Dirac-Hulthen problem

The role of the Hulthen potential on the spin and pseudospin symmetry solutions is investigated systematically by solving the Dirac equation with attractive scalar S(r) and repulsive vector V(r) potentials. The spin and pseudospin symmetry along with orbital dependency (pseudospin-orbit and spin-orbit dependent couplings) of the Dirac equation are included to the solution by introducing the Hulthen-square approximation. This effective approach is based on forming the spin and pseudo-centrifugal kinetic energy term from the square of the Hulthen potential. The analytical solutions of the Dirac equation for the Hulthen potential with the spin-orbit and pseudospin-orbit-dependent couplings are obtained by using the Nikiforov-Uvarov (NU) method. The energy eigenvalue equations and wave functions for various degenerate states are presented for several spin-orbital, pseudospin-orbital and radial quantum numbers under the condition of the spin and pseudospin symmetry. Keywords: Spin and pseudospin symmetry; orbital dependency; Dirac equation; Hulthen potential; Nikiforov-Uvarov Method.Comment: 14 pages and 3 figure

Polynomial Solutions of Shcrodinger Equation with 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.Comment: 14 pages, 2 figures, submitted to Physical Review

Rotational Correction on the Morse Potential Through the Pekeris Approximation and Nikiforov-Uvarov Method

The Nikiforov-Uvarov method is employed to calculate the the Schrodinger equation with a rotation Morse potential. The bound state energy eigenvalues and the corresponding eigenfunction are obtained. All of these calculation present an effective and clear method under a Pekeris approximation to solve a rotation Morse model. Meanwhile the results got here are in a good agreement with ones before.Comment: 11 pages, no figure, submitted to Chemical Physics Letters, (2005

Exact Solutions of the Duffin Kemmer Petiau Equation for the Deformed Hulthen Potential

Using the Nikiforov Uvarov method, an application of the relativistic Duffin Kemmer Petiau equation in the presence of a deformed Hulthen potential is presented for spin zero particles. We derived the first order coupled differential radial equations which enable the energy eigenvalues as well as the full wavefunctions to be evaluated by using of the Nikiforov Uvarov method that can be written in terms of the hypergeometric polynomials.Comment: 8 pages. submitted to Physica Script

An investigation of the temperature dependency of the relative population inversion and the gain in EDFAs by the modified rate equations

The dependence of the relative population inversion in Er3+-doped fiber amplifiers (EDFAs) upon temperature and cross sections, taking into account the amplified spontaneous emission (ASE), are investigated theoretically by the modified rate equation model for 980 nm and 1470 nm pumping conditions. For the temperature range from 0 to +50 oC and at the different signal wavelengths, the temperature and cross section dependent gain characteristics with respect to pump powers are also examined in detail for the both conditions. As a consequence, the dependence of the performance of EDFAs on temperature for 980 nm pumping is weaker than that for 1470 nm pumping, not only at room temperature but also at the temperature range of 0 to +50 oC. However, the performance of EDFAs is more efficient at the pumping wavelength of 1470 nm than that of 980 nm for a wide range of temperature and high-pump powers. The results of this theoretical model are a good agreement with the experimental ones in the literature.Comment: 17 pages, 6 figures. submitted to Optics Communication

Systematical Approach to the Exact Solution of the Dirac Equation for A Special Form of the Woods-Saxon Potential

Exact solution of the Dirac equation for a special form of the Woods-Saxon potential is obtained for the s-states. The energy eigenvalues and two-component spinor wave functions are derived by using a systematical method which is called as Nikiforov-Uvarov. It is seen that the energy eigenvalues strongly depend on the potential parameters. In addition, it is also shown that the non-relativistic limit can be reached easily and directly.Comment: 10 pages, no figures, submitted for Publicatio

A novel angle-dependent potential and its exact solution

The quantum mechanics of a diatomic molecule in a noncentral potential of the type V(r) = V(theta)(theta)/r(2) + V(r)(r) are investigated analytically. The theta-dependent part of the relevant potential is suggested for the first time as a novel angle-dependent (NAD) potential V(theta)(theta) = (h) over bar (2)/2 mu (gamma+beta sin(2) theta+alpha sin(4) theta/sin(2) theta cos(2) theta) and the radial part is selected as the Coulomb potential or the harmonic oscillator potential, i.e., V(r)(r) = -H/r or V(r)(r) = Kr(2), respectively. Exact solutions are obtained in the Schrodinger picture by means of a mathematical method named the Nikiforov-Uvarov (NU). The effect of the angle-dependent part on the solution of the radial part is discussed in several values of the NAD potential's parameters as well as different values of usual quantum numbers

Ro-vibrating energy states of a diatomic molecule in an empirical potential

An approximate analytical solution of the Schrodinger equation is obtained to represent the rotational-vibrational (ro-vibrating) motion of a diatomic molecule. The ro-vibrating energy states arise from a systematical solution of the Schrodinger equation for an empirical potential (EP) V(+/-)(r) = D(e){1-(epsilon/delta)[coth (eta r)](+/- 1)/1-(epsilon/delta)}(2) are determined by means of a mathematical method so-called the Nikiforov-Uvarov (NU). The effect of the potential parameters on the ro-vibrating energy states is discussed in several values of the vibrational and rotational quantum numbers. Moreover, the validity of the method is tested with previous models called the semiclassical (SC) procedure and the quantum mechanical (QM) method. The obtained results are applied to the molecules H(2) and Ar(2)