Bound single-particle states, outgoing resonances and a limited number
of scattering states along a path in the complex kappa-plane (Berggre
n space) are used as a representation to describe the eigenstates of a
realistic nuclear Hamiltonian. It is found that these eigenvectors ar
e contained in the Berggren space, i.e. that the diagonalization of th
e Hamiltonian provides all the bound states and resonances while the r
est of the eigenvalues still remain on the same complex path.