Generalized method of a resolvent operator expansion. III
Miloslav Znojil · Journal of Mathematical Physics · 1980
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.