SUSY transformations with complex factorization constants. Application to spectral singularities

Details SUSY transformations with complex factorization constants. Application to spectral singularities SUSY transformations with complex factorization constants. Application to spectral singularities

2010-06-02

arxiv.org/abs/1006.0282v3

J.Phys.A43:402006,2010

Physics

Mathematical Physics

Thanks to A. Sokolov a number of inaccuracies are corrected

Scientific paper

10.1088/1751-8113/43/40/402006

Supersymmetric (SUSY) transformation operators corresponding to complex factorization constants are analyzed as operators acting in the Hilbert space of functions square integrable on the positive semiaxis. Obtained results are applied to Hamiltonians possessing spectral singularities which are non-Hermitian SUSY partners of selfadjoint operators. A new regularization procedure for the resolution of the identity operator in terms of continuous biorthonormal set of the non-Hermitian Hamiltonian eigenfunctions is proposed. It is also shown that the continuous spectrum eigenfunction has zero binorm (in the sense of distributions) at the singular point.

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