Nikiforov-Uvarov method
Bound States of Spatially Dependent Mass Dirac Equation with the Eckart Potential Including Coulomb Tensor Interaction
Tue, 2015-02-17 16:06 — Sameer. Ikhdair
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TwitterExact Solution of Dirac Equation with Charged Harmonic Oscillator in Electric Field: Bound States
Tue, 2013-10-29 12:46 — Sameer. IkhdairIn some quantum chemical applications, the potential models are linear combination of single exactly solvable potentials. This is the case equivalent of the Stark effect for a charged harmonic oscillator (HO) in a uniform electric field of specific strength (HO in an external dipole field). We obtain the exact s-wave solutions of the Dirac equation for some potential models which are linear combination of single exactly solvable potentials (ESPs). In the framework of the spin and pseudospin symmetric concept, we calculate the analytic energy spectrum and the corresponding two-component upper- and lower-spinors of the two Dirac particles by the Nikiforov-Uvarov (NU) method, in a closed form. The nonrelativistic limit of the solution is also studied and compared with the other works.
Equivalence of the Empirical Shifted Deng–Fan Oscillator Potential for Diatomic Molecules
Tue, 2013-10-29 12:30 — Sameer. IkhdairWe obtain the bound-state solutions of the radial Schrödinger equation with the shifted Deng–Fan oscillator potential in the frame of the Nikiforov-Uvarov method by employing Pekeris-type approximation to deal with the centrifugal term. The analytical expressions for the energy eigenvalues and the corresponding normalized wave functions are obtained in closed form for arbitrary l-state. The ro-vibrational energy levels for a few diatomic molecules are also calculated. They are found to be in good agreement with those ones previously obtained by the Morse potential.
Effects of External Fields on a Two-Dimensional Klein Gordon Particle Under Pseudo-Harmonic Oscillator Interaction
Mon, 2013-09-16 08:20 — Sameer. IkhdairWe study the effects of the perpendicular magnetic and Aharonov-Bohm (AB) flux fields on the energy levels of a two-dimensional (2D) Klein-Gordon (KG) particle subjected to equal scalar and vector pseudo-harmonic oscillator (PHO). We calculate the exact energy eigenvalues and normalized wave functions in terms of chemical potential parameter, magnetic field strength, AB flux field, and magnetic quantum number by means of the Nikiforov-Uvarov (NU) method. The non-relativistic limit, PHO, and harmonic oscillator solutions in the existence and absence of external fields are also obtained.
Approximate κ-state Solutions to the Dirac-Yukawa Problem Based on the Spin and Pseudospin Symmetry
Sun, 2013-09-15 11:09 — Sameer. IkhdairUsing an approximation scheme to deal with the centrifugal (pseudo-centrifugal) term, we solve the Dirac equation with the screened Coulomb (Yukawa) potential for any arbitrary spin-orbit quantum number κ. Based on the spin and pseudospin symmetry, analytic bound state energy spectrum formulas and their corresponding upper- and lower-spinor components of two Dirac particles are obtained using a shortcut of the Nikiforov-Uvarov method. We find a wide range of permissible values for the spin symmetry constant C s from the valence energy spectrum of particle and also for pseudospin symmetry constant C ps from the hole energy spectrum of antiparticle. Further, we show that the present potential interaction becomes less (more) attractive for a long (short) range screening parameter α. To remove the degeneracies in energy levels we consider the spin and pseudospin solution of Dirac equation for Yukawa potential plus a centrifugal-like term. A few special cases such as the exact spin (pseudospin) symmetry Dirac-Yukawa, the Yukawa plus centrifugal-like potentials, the limit when α becomes zero (Coulomb potential field) and the non-relativistic limit of our solution are studied. The nonrelativistic solutions are compared with those obtained by other methods.
Approximate Analytical Solutions of the Generalized Woods-Saxon Potentials Including the Spin-Orbit Coupling Term and Spin Symmetry
Sun, 2013-09-15 10:44 — Sameer. IkhdairWe study the approximate analytical solutions of the Dirac equation for the generalized Woods-Saxon potential with the pseudo-centrifugal term. We apply the Nikiforov-Uvarov method (which solves a second-order linear differential equation by reducing it to a generalized hypergeometric form) to spin- and pseudospin-symmetry to obtain, in closed form, the approximately analytical bound state energy eigenvalues and the corresponding upper- and lower-spinor components of two Dirac particles. The special cases κ = ±1 (s = = 0, s-wave) and the non-relativistic limit can be reached easily and directly for the generalized and standard Woods-Saxon potentials. We compare the non-relativistic results with those obtained by others.
A Semi-Relativistic Treatment of Spinless Particles Subject to the Nuclear Woods-Saxon Potential
Thu, 2013-09-12 11:14 — Sameer. IkhdairBy applying an appropriate Pekeris approximation to deal with the centrifugal term, we present an approximate systematic solution of the two-body spinless Salpeter (SS) equation with the Woods-Saxon interaction potential for an arbitrary l-state. The analytical semi-relativistic bound-state energy eigenvalues and the corresponding wave functions are calculated. Two special cases from our solution are studied: the approximated Schrödinger-Woods-Saxon problem for an arbitrary l-state and the exact s-wave (l=0).
Two Approximation Schemes to The Bound States of the Dirac–Hulthén Problem
Thu, 2013-09-12 11:06 — Sameer. IkhdairThe bound-state (energy spectrum and two-spinor wavefunctions) solutions of the Dirac equation with the Hulthén potential for all angular momenta based on the spin and pseudospin symmetry are obtained. The parametric generalization of the Nikiforov–Uvarov method is used in the calculations. The orbital dependence (spin–orbit- and pseudospin–orbit-dependent coupling too singular 1/r2) of the Dirac equation are included to the solution by introducing a more accurate approximation scheme to deal with the centrifugal (pseudo-centrifugal) term. The approximation is also made for the less singular 1/r orbital term in the Dirac equation for a wider energy spectrum. The nonrelativistic limits are also obtained on mapping of parameters.
Approximate l-state solutions of the D-dimensional Schrödinger equation for Manning-Rosen potential
Wed, 2013-09-11 14:08 — Sameer. IkhdairThe Schrödinger equation in D-dimensions for the Manning-Rosen potential with the centrifugal term is solved approximately to obtain bound states eigensolutions (eigenvalues and eigenfunctions). The NikiforovUvarov (NU) method is used in the calculations. We present numerical calculations of energy eigenvalues to two- and four-dimensional systems for arbitrary quantum numbers n and l with three different values of the potential parameter α. It is shown that because of the interdimensional degeneracy of eigenvalues, we can also reproduce eigenvalues of a upper/lower dimensional system from the well-known eigenvalues of a lower/upper dimensional system by means of the transformation (n, l, D) → (n, l ±1,D∓2). This solution reduces to the Hulthén potential case.
Exact Solution of the Klein-Gordon Equation for the PT-Symmetric Generalized Woods-Saxon Potential by the Nikiforov-Uvarov Method
Wed, 2013-09-11 10:41 — Sameer. IkhdairThe one-dimensional Klein-Gordon (KG) equation has been solved for the PT-symmetric generalized Woods-Saxon (WS) potential. The Nikiforov-Uvarov(NU} method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type is used to obtain exact energy eigenvalues and corresponding eigenfunctions. We have also investigated the positive and negative exact bound states of the s-states for different types of complex generalized WS potentials.
