SUSY transformations for quasinormal modes of open systems

Supersymmetry (SUSY) in quantum mechanics is extended from square-integrabl e states to those satisfying the outgoing-wave boundary condition, in a Kle in-Gordon formulation. This boundary condition allows both the usual normal modes and quasinormal modes with complex eigenvalues omega. The simple gen eralization leads to three features: The counting of eigenstates under SUSY becomes more systematic; the linear-space structure of outgoing waves (non trivially different from the usual Hilbert space of square-integrable state s) is preserved by SUSY; and multiple states at the same frequency (not all owed for normal modes) are also preserved. The existence or otherwise of SU SY partners is furthermore relevant to the question of inversion: Are open systems uniquely determined by their complex outgoing-wave spectra? (C) 200 1 American Institute of Physics.