Bound-state energies of the exponentially screened static and cosine Coulombic potentials

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Abstract
Bound state energies of the exponentially screened Coulomb potentials: V (r) =−Ze−αr cosεαr/r, static (ε=0) and oscillatory (ε=1), are obtained by a perturbation calculation on the basis of the Hulthén functions. Closed form expressions of the perturbative matrix elements as well as of the Hulthén functions, for ’’S’’ states and for l≠0 states (with an approximated rotational term), are obtained by the ladder operator method. When varying the values of the Hulthén parameter, the first order perturbed eigenvalues of the screened potentials are found to be close to the exact values. New results (l≠0) are given for the cosine case.