Matrix technique for nonperturbative Green function of time-independent Schrödinger equation

Abstract

A Green function of time-independent multi-channel Schrödinger equation is considered in matrix representation beyond a perturbation theory. Nonperturbative Green functions are obtained through the regular in zero and at infinity solutions of the multi-channel Schrödinger equation for different cases of symmetry of the full Hamiltonian. The spectral expansions for the nonperturbative Green functions are obtained in simple form through multi-channel wave functions. The developed approach is applied to obtain simple analytic equations for the Green functions and transition matrix elements for compound multi-potential system within quasi-classical approximation. The limits of strong and weak inter-channel interactions are studied. (2000): 15A90, 34B27, 39B42. Mathematics Subject Classifications