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SUSY transformations for quasinormal modes of open systems. (English) Zbl 1017.81018
Summary: 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 \(\omega\). 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?

MSC:
81Q60 Supersymmetry and quantum mechanics
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