Two approximation schemes to the bound states of the Dirac-Hulthén problem. (English) Zbl 1227.81160

Ikhdair, Sameer M.; Sever, Ramazan

J. Phys. A, Math. Theor. 44, No. 35, Article ID 355301, 29 p. (2011).

Summary: The 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 \(1/r^{2}\)) 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. Nonrelativistic limits are also obtained on the mapping of the parameters.

MSC:

81Q05	Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81Q10	Selfadjoint operator theory in quantum theory, including spectral analysis
34C14	Symmetries, invariants of ordinary differential equations
81Q60	Supersymmetry and quantum mechanics
81R05	Finite-dimensional groups and algebras motivated by physics and their representations
34L40	Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
81V35	Nuclear physics