Non-Hermitian Quantum Mechanics of Non-diagonalizable Hamiltonians: puzzles with self-orthogonal states
Abstract
We consider QM with non-Hermitian quasi-diagonalizable Hamiltonians, i.e. the Hamiltonians having a number of Jordan cells in particular biorthogonal bases. The "self-orthogonality" phenomenon is clarified in terms of a correct spectral decomposition and it is shown that "self-orthogonal" states never jeopardize resolution of identity and thereby quantum averages of observables. The example of a complex potential leading to one Jordan cell in the Hamiltonian is constructed and its origin from level coalescence is elucidated. Some puzzles with zero-binorm bound states in continuous spectrum are unraveled with the help of a correct resolution of identity.
Keywords
Cite
@article{arxiv.quant-ph/0602207,
title = {Non-Hermitian Quantum Mechanics of Non-diagonalizable Hamiltonians: puzzles with self-orthogonal states},
author = {A. V. Sokolov and A. A. Andrianov and F. Cannata},
journal= {arXiv preprint arXiv:quant-ph/0602207},
year = {2016}
}
Comments
25 pages, one subsection and an appendix added, terminology is refined, important refs.added