Representation of a complex Green function on a real basis: Integral representation - art. no. 062705

摘要

We describe a decomposition of the resolvent G(E)=1/(E-H) into two parts, G(int)(E) and G(ext)(E), each of which can be computed, potentially, with moderate cost. Using an integral representation, G(int)(E) is built from a Hermitian Hamiltonian matrix constructed on a real discrete basis, and it incorporates the interaction in the interior region where the dynamics take place. The term G(ext)(E) takes into account the flux passing into the exterior region, and it can be replaced by a Pade approximant by means of a simple connection between G(int)(E) and G(ext)(E). We illustrate the method by application to the examples of photoionization of a hydrogen atom and scattering of a particle from a l/(l + r)(4) potential. [References: 13]