  Supersymmetry (SUSY) in quantum mechanics is extended from square-integrable
states to those satisfying the outgoing-wave boundary condition, in a
Klein-Gordon formulation. This boundary condition allows both the usual normal
modes and quasinormal modes with complex eigenvalues. The simple generalization
leads to three features: the counting of eigenstates under SUSY becomes more
systematic; the linear-space structure of outgoing waves (nontrivially
different from the usual Hilbert space of square-integrable states) is
preserved by SUSY; and multiple states at the same frequency (not allowed for
normal modes) are also preserved. The existence or otherwise of SUSY partners
is furthermore relevant to the question of inversion: are open systems uniquely
determined by their complex outgoing-wave spectra?
