GENERALIZED-METHOD OF A RESOLVENT OPERATOR EXPANSION .3.

We show that our Born-like parametrized expansion of R (E) = (E - H) -1 is, after minor modifications, well defined even at the pole of R (E) and provides a new method of solving linear homogeneous equations. Three different possibilities of application are discussed here: (1) An analytic method of solving the differential eauations. It is based on the partitioning of generalized power series and illustrated by the new solution of the s-wave Schrödinger equation. (2) A consequent model space reduction of Schrödinger equation. In terms of the matrix moments of H, the effective interaction is defined as an operator continued fraction. (3) A new form of the perturbation theory which dispenses with the solution of the unperturbed problem. © 1980 American Institute of Physics.