SUSY transformations with complex factorization constants. Application to spectral singularities

Autor:	Samsonov, Boris F.
Rok vydání:	2010
Předmět:	Mathematical Physics High Energy Physics - Theory Quantum Physics
Zdroj:	J.Phys.A43:402006,2010
Druh dokumentu:	Working Paper
DOI:	10.1088/1751-8113/43/40/402006
Popis:	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. Comment: Thanks to A. Sokolov a number of inaccuracies are corrected
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1006.0282 Zobrazit plný text záznamu View this record from Arxiv