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A detailed study of the bound-state properties of the Hulth\'en potential is presented. Accurate eigenenergies are obtained for the Hulth\'en potential by numerical integration of the Schr\"odinger equation. One-parameter variational calculations are carried out. The variational results are practically identical to the exact energies, except in the high-screening region. The critical screening parameter is calculated for various values of l for n10 by a numerical solution of the wave equation. The energy eigenvalues obtained by a variety of methods are compared and discussed. The variational wave functions are employed to calculate absorption oscillator strengths for 1s2p, 1s3p, and 2p3d transitions.
Y. P. Varshni (Tue,) studied this question.