The padé approximant method for finding the Hilbert-Schmidt eigenvalues and eigenfunctions in two- and three-body problems

An approach is proposed which makes it possible to obtain the Hilbert-Schmidt (or Sturm-Liouville) eigenvalue and eigenfunctions for two- or three-body systems over the entire domain of analyticity of these functions in energy on the basis of calculations of bound states only. It is shown how this method may be used to find the two- and three-body resonances and the near-threshold states.