Non-linear Supersymmetry for non-Hermitian, non-diagonalizable Hamiltonians: II. Rigorous results
arXiv:math-ph/0610022 · doi:10.1016/j.nuclphysb.2007.03.015
Abstract
We continue our investigation of the nonlinear SUSY for complex potentials started in the Part I (math-ph/0610024) and prove the theorems characterizing its structure in the case of non-diagonalizable Hamiltonians. This part provides the mathematical basis of previous studies. The classes of potentials invariant under SUSY transformations for non-diagonalizable Hamiltonians are specified and the asymptotics of formal eigenfunctions and associated functions are derived. Several results on the normalizability of associated functions at infinities are rigorously proved. Finally the Index Theorem on relation between Jordan structures of intertwined Hamiltonians depending of the behavior of elements of canonical basis of supercharge kernel at infinity is proven.
31 pp., comments on PT symmetry and few relevant refs are added
References in corpus (4)
Cited by in corpus (10)
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- Spectral singularities for Non-Hermitian one-dimensional Hamiltonians: puzzles with resolution of identity
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- Spectral Design for Matrix Hamiltonians: Different Methods of Constructing of a Matrix Intertwining Operator
- Minimal Realizations of Supersymmetry for Matrix Hamiltonians
- Equivalent Hermitian operator from supersymmetric quantum mechanics
- Factorization of non-linear supersymmetry in one-dimensional Quantum Mechanics. II: proofs of theorems on reducibility
- Resolutions of Identity for Some Non-Hermitian Hamiltonians. I. Exceptional Point in Continuous Spectrum
- Polynomial supersymmetry for matrix Hamiltonians: proofs