Complex-scaled spectrum completeness for pedestrians

摘要

The Complex Scaling Method (CSM) is rephrased in terms of a Hamiltonian containing an optical potential. Traditional theorems concerning Jost solutions, the Jost function, residues of a suitable Green's function at its poles, and the resolution of the identity are extended. Elementary derivations of the completeness of the CSM spectrum are detailed for the one and the two channel cases. (C) 2003 Elsevier Science (USA). All rights reserved. [References: 11]