Representation of a complex Green function on a real basis
Robin Shakeshaft, Bernard Piraux · arXiv (Cornell University) · 1999
When the Hamiltonian H 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 H 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. Specifically, we show that the resolvent has a series representation whose terms can be computed recursively and rapidly.