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

81Q05Closed and approximate solutions to quantum-mechanical equations
81Q10Selfadjoint operator theory in quantum theory, including spectral analysis
34C14Symmetries, invariants (ODE)
81Q60Supersymmetry and quantum mechanics
81R05Representations of finite-dimensional groups and algebras in quantum theory
34L40Particular ordinary differential operators
81V35Applications of quantum theory to nuclear physics
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