Two approximation schemes to the bound states of the Dirac-Hulthen problem

Sever, Ramazan
The bound-state (energy spectrum and two-spinor wavefunctions) solutions of the Dirac equation with the Hulthen 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/r(2)) 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.


Pseudospin symmetry solution of the Dirac equation with an angle-dependent potential
Berkdemir, Cueneyt; Sever, Ramazan (IOP Publishing, 2008-02-01)
The pseudospin symmetry solution of the Dirac equation for spin 1/2 particles moving within the Kratzer potential connected with an angle-dependent potential is investigated systematically. The Nikiforov-Uvarov method is used to solve the Dirac equation. All of the studies are performed for the exact pseudospin symmetry (SU2) case and also the exact spin symmetry case is given briefly in the appendix. Bound-state solutions are presented to discuss the contribution of the angle-dependent potential to the rel...
Green's matrix for a second-order self-adjoint matrix differential operator
Sisman, Tahsin Cagri; Tekin, Bayram (IOP Publishing, 2010-03-26)
A systematic construction of the Green's matrix for a second-order self-adjoint matrix differential operator from the linearly independent solutions of the corresponding homogeneous differential equation set is carried out. We follow the general approach of extracting the Green's matrix from the Green's matrix of the corresponding first-order system. This construction is required in the cases where the differential equation set cannot be turned to an algebraic equation set via transform techniques.
An alternative simple solution of the sextic anharmonic oscillator and perturbed coulomb problems
IKHDAİR, SAMEER; Sever, Ramazan (World Scientific Pub Co Pte Lt, 2007-10-01)
Utilizing an appropriate ansatz to the wave function, we reproduce the exact bound-state solutions of the radial Schrodinger equation to various exactly solvable sextic an-harmonic oscillator and confining perturbed Coulomb models in D-dimensions. We show that the perturbed Coulomb problem with eigenvalue E can be transformed to a sextic anharmonic oscillator problem with eigenvalue P. We also check the explicit relevance of these two related problems in higher-space dimensions. It is shown that exact solut...
A new integrable generalization of the Korteweg-de Vries equation
Karasu-Kalkanli, Ayse; Karasu, Atalay; Sakovich, Anton; Sakovich, Sergei; TURHAN, REFİK (AIP Publishing, 2008-07-01)
A new integrable sixth-order nonlinear wave equation is discovered by means of the Painleve analysis, which is equivalent to the Korteweg-de Vries equation with a source. A Lax representation and an auto-Backlund transformation are found for the new equation, and its traveling wave solutions and generalized symmetries are studied. (C) 2008 American Institute of Physics.
Exact solutions for vibrational levels of the Morse potential
Taşeli, Hasan (IOP Publishing, 1998-01-16)
The vibrational levels of diatomic molecules via Morse potentials are studied by means of the system confined in a spherical box of radius l, II is shown that there exists a critical radius l(cr),, at which the spectrum of the usual unbounded system can be calculated to any desired accuracy. The results are compared with those of Morse's classical solution which is based on the assumption that the domain of the internuclear distance r includes the unphysical region (-infinity, 0). By determining numerically...
Citation Formats
S. IKHDAİR and R. Sever, “Two approximation schemes to the bound states of the Dirac-Hulthen problem,” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, pp. 0–0, 2011, Accessed: 00, 2020. [Online]. Available: