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

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

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

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

Shape-invariance approach and Hamiltonian hierarchy method on the Woods-Saxon potential for l not equal 0 states

An analytically solvable Woods-Saxon potential for l not equal 0 states is presented within the framework of Supersymmetric Quantum Mechanics formalism. The shape-invariance approach and Hamiltonian hierarchy method are included in calculations by means of a translation of parameters. The approximate energy spectrum of this potential is obtained for l not equal 0 states, applying the Woods-Saxon square approximation to the centrifugal barrier term of the Schrodinger equation

Bound state solutions of the Schrodinger equation for modified Kratzer's molecular potential

We present the arbitrary angular momentum solutions of the Schrodinger equation for a diatomic molecule with the modified Kratzer potential D-e[(r - r(e))/r](2). The bound state energy eigenvalues and the corresponding eigenfunctions are obtained by the use of the Nikiforov-Uvarov (NU) method which is related to the solutions in terms of Jacobi polynomials. The bound states are calculated for various values of l with n <= 5 and applied to several diatomic molecules. All of these calculations present an effective and methodological procedure under the NU method to investigate the Kratzer's molecular systems. (c) 2005 Elsevier B.V. All rights reserved

Effect of growth rate and Mg content on dendrite tip characteristics of Al-Cu-Mg ternary alloys

An experimental analysis is presented to correlate the secondary dendrite arm spacing lambda (2) and dendrite tip radius R with growth rate V and Mg content C (0-Mg) of Al-Cu-Mg ternary alloys. Under constant temperature gradient G (4.84 +/- 0.13 K mm(-1)), a series of directional solidification experiments were performed at five different growth rates V (16.7-83.3 mu m/s) and five different Mg contents C (0-Mg) in Al-5 wt.% Cu-(0.5-5) wt.% Mg alloys. Solid-liquid interface was investigated from the longitudinal sections of the quenched samples, and lambda (2) and R were measured on the dendrite tips. The dependencies of lambda (2) and R on V and C (0-Mg) were determined. The experimental results showed that the values of lambda (2) and R decrease as V and C (0-Mg) increase at a constant G. The present exponent values related to V are found to be slightly lower than the values of the theoretical models and previous experimental works; however, C (0-Mg) exponent values are found to be much lower than the theoretical models and previous experimental works. The ratio of the secondary dendrite arm spacing to the dendrite tip radius is 2.09 +/- 0.15, in good agreement with the scaling law. At a constant C (0-Mg), the values of VR (2) were found to slightly increase with the ascending V. However, as C (0-Mg) increases, the values of VR (2) decrease