Representation of a complex Green function on a real basis: I. General Theory
arXiv:physics/9909028 · doi:10.1103/PhysRevA.62.062705
Abstract
When the Hamiltonian of a system is represented by a finite matrix, constructed from a discrete basis, the matrix representation of the resolvent covers only one branch. We show how all branches can be specified by the phase of a complex unit of time. This permits the Hamiltonian matrix to be constructed on a real basis; the only duty of the basis is to span the dynamical region of space, without regard for the particular asymptotic boundary conditions that pertain to the problem of interest.
about 40 pages with 5 eps-figures