An exact path-integral treatment of the s states for the Hulth\'en potential is presented. A procedure of the nontrivial change of variable accompanied by the local time rescaling is given in detail. The dimensional extension trick is applied to convert the radial path integral into a path integral in the SU(2) manifold. The exact energy spectrum and the normalized s-state eigenfunctions are obtained from the poles of the Green function and their residues, respectively. The Yukawa and the Coulomb limits are also discussed.
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Cai et al. (1986) studied this question.
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