Resonance states as solutions of the Schrödinger equation with a nonlocal boundary condition

Resonance states of a system consisting of a particle interacting with a finite-range potential are introduced in a novel way, independent of the notion of scattering. It is shown that a resonance wave function satisfies a certain nonlocal boundary condition on the surface that delimits the range of the potential. With a central potential our general boundary condition reduces to a set of local ones that are identical with those obtained previously by Humblet and Rosenfeld by different methods.