Cüneyt Berkdemir

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.

Exact solutions of the Schrödinger equation with non-central potential by the Nikiforov–Uvarov method

The general solutions of the Schrodinger equation for a non-central potential are obtained by using the Nikiforov–Uvarov method. The Schrodinger equation with general non-central potential is separated into radial and angular parts, and energy eigenvalues and eigenfunctions are derived analytically. By making special selections, the non-central potential is reduced to Coulomb and Hartmann ring-shaped potentials, and the obtained results are compared with the solutions of Coulomb and Hartmann potentials given in the literature.

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 first-order coupled differential radial equations which enable the energy eigenvalues as well as the full wavefunctions to be evaluated by using the Nikiforov–Uvarov method that can be written in terms of hypergeometric polynomials.

On the exact solutions of the Dirac equation with a novel angle-dependent potential

We study the problem of the relativistic motion of a 1/2-spin particle in an exactly solvable potential, which consists of the harmonic oscillator potential plus a novel angle-dependent potential, The analytic bound state solutions of the Dirac equation for this potential are obtained by using the Nikiforov–Uvarov method. The wave functions of the radial and angle-dependent parts of the Dirac equation are derived in the form of the Laguerre and Jacobi polynomials. The contribution of the angle-dependent potential to the relativistic energy spectra is discussed under the condition that the scalar potential is equal to or minus the vector potential.

Systematical approach to the exact solution of the Dirac equation for a deformed form of the Woods–Saxon potential

The exact solution of the Dirac equation for a deformed form of the Woods–Saxon potential is obtained for the s-wave relativistic energy spectrum. The energy eigenvalues and two-component spinor wavefunctions are derived analytically by using a systematical method which is called Nikiforov–Uvarov. It is seen that the energy eigenvalues and the wavefunctions strongly depend on the parameters of the potential. In addition, it is also shown that the non-relativistic limit can be reached easily and directly for a special case of the standard Woods–Saxon potential.

Spin and pseudospin symmetry along with orbital dependency of the Dirac–Hulthén problem

Abstract 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.

The temperature dependent performance analysis of EDFAs pumped at 1480 nm: A more accurate propagation equation.

An analytically expression for the temperature dependence of the signal gain of an erbium-doped fiber amplifier (EDFA) pumped at 1480 nm are theoretically obtained by solving the propagation equations with the amplified spontaneous emission (ASE). It is seen that the temperature dependence of the gain strongly depends on the distribution of population of Er3+-ions in the second level. In addition, the output pump power and the intrinsic saturation power of the signal beam are obtained as a function of the temperature. Numerical calculations are carried out for the temperature range from - 20 to + 60 oC and the various fiber lengths. But the other gain parameters, such as the pump and signal wavelengths and their powers, are taken as constants. It is shown that the gain decreases with increasing temperature within the range of L </= 27 m.

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

Abstract The dependence of the relative population inversion in Er 3+ -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 and 1470 nm pumping conditions. For the temperature range from 0 to ±50 °C 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 from 0 to ±50 °C. 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 higher-pump power levels. The results of this theoretical model are a good agreement with the experimental ones in the literature.

EIGENVALUES AND EIGENFUNCTIONS OF WOODS–SAXON POTENTIAL IN PT-SYMMETRIC QUANTUM MECHANICS

Using the Nikiforov–Uvarov method which is based on solving the second-order differential equations, we firstly analyzed the energy spectra and eigenfunctions of the Woods–Saxon potential. In the framework of the PT-symmetric quantum mechanics, we secondly solved the time-independent Schrodinger equation for the PT and non-PT-symmetric version of the potential. It is shown that the discrete energy eigenvalues of the non-PT-symmetric potential consist of the real and imaginary parts, but the PT-symmetric one has a real spectrum. Results are obtained for s-states only.

On the Temperature-Dependent Gain and Noise Figure Analysis of C-Band High-Concentration EDFAs With the Effect of Cooperative Upconversion

We present an efficient temperature-dependent analysis to study the effect of cooperative upconversion on the temperature-dependent gain (TDG) performance of the C-band erbium-doped fiber amplifier (EDFA) at high-concentration. The influence of cooperative upconversion on the TDG is examined by using a set of temperature-dependent rate and light propagation equations. In the analysis given, the amplified spontaneous emission (ASE), as well as the excited state absorption (ESA) are also considered. In the forward pumping configuration at a signal wavelength of 1547 nm and in the temperature range of - 40degC to + 80degC, the variations of the TDG and the noise figure (NF) are about 1.7 and 0.9 dB, respectively. Numerical analysis results show that, with 260-mW/1480-nm pump power, an erbium-doped fiber amplifier having a doping concentration of 4.4 times 1026 ion/m3 and optimum length of 9.2 cm may reach a signal gain of 44.6 dB and a noise figure of 3.9 dB at room temperature.