Dirac equation
Relativistic Bound States in the Presence of Spherically Ring-Shaped Q-Deformed Woods–Saxon Potential With Arbitrary l-States
Tue, 2013-10-29 10:41 — Sameer. IkhdairApproximate bound-state solutions of the Dirac equation with q-deformed Woods–Saxon (WS) plus a new generalized ring-shaped (RS) potential are obtained for any arbitrary l-state. The energy eigenvalue equation and corresponding two-component wave functions are calculated by solving the radial and angular wave equations within a shortcut of the Nikiforov–Uvarov (NU) method. The solutions of the radial and polar angular parts of the wave function are expressed in terms of the Jacobi polynomials. A new approximation being expressed in terms of the potential parameters is carried out to deal with the strong singular centrifugal potential term l(l+1)r-2. Under some limitations, we can obtain solution for the RS Hulthén potential and the standard usual spherical WS potential (q = 1).
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TwitterSpin And Pseudospin Symmetries In Relativistic Trigonometric Pöschl Teller Potential With Centrifugal Barrier
Tue, 2013-10-29 09:00 — Sameer. IkhdairApproximate analytical solutions of the Dirac equation with the trigonometric Pöschl–Teller (tPT) potential are obtained for arbitrary spin-orbit quantum number κ using an approximation scheme to deal with the spin-orbit coupling terms κ(κ±1)r-2. In the presence of exact spin and pseudo-spin (p-spin) symmetric limitation, the bound state energy eigenvalues and the corresponding two-component wave functions of the Dirac particle moving in the field of attractive and repulsive tPT potential are obtained using the parametric generalization of the Nikiforov–Uvarov (NU) method. The case of nonrelativistic limit is studied too.
Relativistic Symmetries with the Trigonometric Pöschl—Teller Potential Plus Coulomb-Like Tensor Interaction
Mon, 2013-09-16 10:57 — Sameer. IkhdairThe Dirac equation is solved to obtain its approximate bound states for a spin-1/2 particle in the presence of trigonometric Pöschl—Teller (tPT) potential including a Coulomb-like tensor interaction with arbitrary spin—orbit quantum number κ using an approximation scheme to substitute the centrifugal terms κ(κ ± 1)r−2. In view of spin and pseudo-spin (p-spin) symmetries, the relativistic energy eigenvalues and the corresponding two-component wave functions of a particle moving in the field of attractive and repulsive tPT potentials are obtained using the asymptotic iteration method (AIM). We present numerical results in the absence and presence of tensor coupling A and for various values of spin and p-spin constants and quantum numbers n and κ. The non-relativistic limit is also obtained.
Relativistic Symmetry of Position-Dependent Mass Particles in A Coulomb Field Including Tensor Interaction
Mon, 2013-09-16 07:43 — Sameer. IkhdairThe spatially-dependent mass Dirac equation is solved exactly for attractive scalar and repulsive vector Coulomb potentials, including a tensor interaction under the spin and pseudospin symmetric limits. Closed forms of the energy eigenvalue equation and wave functions are obtained for arbitrary spin—orbit quantum number κ. Some numerical results are also given, and the effect of tensor interaction on the bound states is presented. It is shown that tensor interaction removes the degeneracy between two states in the spin doublets. We also investigate the effects of the spatially-dependent mass on the bound states under spin symmetric limit conditions in the absence of tensor interaction.
Approximate Analytical Solutions to Relativistic Andnonrelativistic Pöschl–Teller Potential with its Thermodynamic Properties
Sun, 2013-09-15 13:42 — Sameer. IkhdairWe apply the asymptotic iteration method (AIM) to obtain the solutions of Schrodinger equation in the presence of Poschl-Teller (PT) potential. We also obtain the solutions of Dirac equation for the same potential under the condition of spin and pseudospin (p-spin) symmetries. We show that in the nonrelativistic limits, the solution of Dirac system converges to that of Schrodinger system. Rotational-Vibrational energy eigenvalues of some diatomic molecules are calculated. Some special cases of interest are studied such as s-wave case, reflectionless-type potential and symmetric hyperbolic PT potential. Furthermore, we present a high temperature partition function in order to study the behavior of the thermodynamic functions such as the vibrational mean energy U, specific heat C, free energy F and entropy S.
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.
Effect of Tensor Interaction in the Dirac-Attractive Radial Problem Under Pseudospin Symmetry Limit
Sun, 2013-09-15 10:16 — Sameer. IkhdairSpin and Pseudospin Symmetry Along with Orbital Dependency of the Dirac–Hulthén Problem
Sun, 2013-09-15 09:15 — Sameer. IkhdairThe role of the Hulthén potential on the spin and
pseudospin symmetry solutions is investigated systematically by solving
the Dirac equation with attractive scalar 
and repulsive vector 
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
Hulthén-square approximation. This effective approach is based on
forming the spin and pseudo-centrifugal kinetic energy term from the
square of the Hulthén potential. The analytical solutions of the Dirac
equation for the Hulthén 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.
Solutions of The Spatially-Dependent Mass Dirac Equation with the Spin and Pseudospin Symmetry for the Coulomb-Like Potential
Sun, 2013-09-15 08:32 — Sameer. IkhdairWe study the effect of spatially dependent mass function over the solution of the Dirac equation with the Coulomb potential in the (3+1)-dimensions for any arbitrary spin-orbit κ state. In the framework of the spin and pseudospin symmetry concept, the analytic bound state energy eigenvalues and the corresponding upper and lower two-component spinors of the two Dirac particles are obtained by means of the Nikiforov-Uvarov method, in closed form. This physical choice of the mass function leads to an exact analytical solution for the pseudospin part of the Dirac equation. The special cases (l=l˜=0, i.e., s-wave), the constant mass and the non-relativistic limits are briefly investigated.
