Many-body Coulomb problem in the phase-energy representation

The many-body quantum-mechanical Coulomb problem is exactly reformulated in a "phase-energy" representation. Rather than solving for a many-component wave-function, this formulation focuses on a set of eigenphases that document the evolution of a system from its compact to its fragmented limit. The eigenphases in rum hinge on the explicit evaluation of kinetic and potential energies as the system wolves. An illustration using the doubly excited states of helium shows that information on the nature of the eigenchannels is encoded in these energies.