Nikiforov and Uvarov method
Polynomial Solution of Non-Central Potentials
Tue, 2013-10-29 10:06 — Sameer. IkhdairWe show that the exact energy eigenvalues and eigenfunctions of the Schrodinger equation for charged particles moving in certain class of non-central potentials can be easily calculated analytically in a simple and elegant manner by using Nikiforov and Uvarov (NU) method. We discuss the generalized Coulomb and harmonic oscillator systems. We study the Hartmann Coulomb and the ring-shaped and compound Coulomb plus Aharanov-Bohm potentials as special cases. The results are in exact agreement with other methods.
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TwitterExact Bound States of the D-Dimensional Klein Gordon Equation with Equal Scalar and Vector Ring-Shaped Pseudoharmonic Potential
Mon, 2013-10-28 13:34 — Sameer. IkhdairWe present the exact solution of the Klein–Gordon equation in D-dimensions in the presence of the equal scalar and vector pseudoharmonic potential plus the ring-shaped potential using the Nikiforov–Uvarov method. We obtain the exact bound state energy levels and the corresponding eigen functions for a spin-zero particles. We also find that the solution for this ring-shaped pseudoharmonic potential can be reduced to the three-dimensional (3D) pseudoharmonic solution once the coupling constant of the angular part of the potential becomes zero.
Exact Solutions of the Modified Kratzer Potential Plus Ring-Shaped Potential in the D-Dimensional Schrödinger Equation by the Nikiforov Uvarov Method
Mon, 2013-10-28 13:27 — Sameer. IkhdairWe present analytically the exact energy bound-states solutions of the Schrodinger equation in D-dimensions for a recently proposed modified Kratzer potential plus ring-shaped potential by means of the conventional Nikiforov-Uvarov method. We give a clear recipe of how to obtain an explicit solution to the wave functions in terms of orthogonal polynomials. The results obtained in this work are more general and true for any dimension which can be reduced to the standard forms in three-dimensions given by other works.
Exact Solutions of the D-dimensional Schrödinger Equation for a Ring–shaped Pseudoharmonic Potential
Sun, 2013-09-15 12:03 — Sameer. IkhdairA new non-central potential, consisting of a pseudoharmonic potential plus another recently proposed ring-shaped potential, is solved. It has the form . The energy eigenvalues and eigenfunctions of the bound-states for the Schrödinger equation in D-dimensions for this potential are obtained analytically by using the Nikiforov-Uvarov method. The radial and angular parts of the wave functions are obtained in terms of orthogonal Laguerre and Jacobi polynomials. We also find that the energy of the particle and the wave functions reduce to the energy and the wave functions of the bound-states in three dimensions.
Relativistic Solution in D-Dimensions to a Spin-Zero Particle for Equal Scalar and Vector Ring-Shaped Kratzer Potential
Sun, 2013-09-15 10:14 — Sameer. IkhdairThe Klein-Gordon equation in D-dimensions for a recently proposed ring-shaped Kratzer potential is solved analytically by means of the conventional Nikiforov-Uvarov method. The exact energy bound states and the corresponding wave functions of the Klein-Gordon are obtained in the presence of the non-central equal scalar and vector potentials. The results obtained in this work are more general and can be reduced to the standard forms in three dimensions given by other works.
