Padé phenomenology for two-body bound states

Padé approximants in the squared momentum variable, recently used for elastic scattering, are employed in generating accurate analytic approximants for bound states. Through iteration, [$\frac{L}{L+1\mathrm{}}$] approximants yield the lowest eigenstate of the homogeneous Lippmann-Schwinger equation for Yukawa, Malfliet-Tjon, and Reid soft core central potentials with, respectively, $L=1, 2, \mathrm{and} 3$. Higher eigenstates are readily obtained; the second is given for the Yukawa potential. Analytic separable expansions and scattering expressions result.