SUSY Transformations for Quasinormal Modes of Open Systems

Details SUSY Transformations for Quasinormal Modes of Open Systems SUSY Transformations for Quasinormal Modes of Open Systems

2000-11-23

arxiv.org/abs/math-ph/0011037v1

J. Math. Phys. _42_, 4802 (2001)

Physics

Mathematical Physics

14 pages, 4 figures

Scientific paper

10.1063/1.1388900

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?

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