dorsal/arxiv
View SchemaNon-Hermitian Quantum Mechanics of Non-diagonalizable Hamiltonians: puzzles with self-orthogonal states
| Authors | A. V. Sokolov, A. A. Andrianov, F. Cannata |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0602207 |
| URL | https://arxiv.org/abs/quant-ph/0602207 |
| DOI | 10.1088/0305-4470/39/32/S20 |
| Journal | J.Phys. A39 (2006) 10207-10228 |
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.
{
"annotation_id": "35ec5f29-2404-492c-873b-ec24c35c45e9",
"date_created": "2026-03-02T18:02:24.079000Z",
"date_modified": "2026-03-02T18:02:24.079000Z",
"file_hash": "e7bcbbe9c67943825cec2929b1ba0d55c639142943d4fba6262cc1e7f6eaf0d6",
"private": false,
"record": {
"abstract": "We consider QM with non-Hermitian quasi-diagonalizable Hamiltonians, i.e. the\nHamiltonians having a number of Jordan cells in particular biorthogonal bases.\nThe \"self-orthogonality\" phenomenon is clarified in terms of a correct spectral\ndecomposition and it is shown that \"self-orthogonal\" states never jeopardize\nresolution of identity and thereby quantum averages of observables. The example\nof a complex potential leading to one Jordan cell in the Hamiltonian is\nconstructed and its origin from level coalescence is elucidated. Some puzzles\nwith zero-binorm bound states in continuous spectrum are unraveled with the\nhelp of a correct resolution of identity.",
"arxiv_id": "quant-ph/0602207",
"authors": [
"A. V. Sokolov",
"A. A. Andrianov",
"F. Cannata"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech",
"hep-th",
"math-ph",
"math.MP",
"physics.atom-ph",
"physics.chem-ph"
],
"doi": "10.1088/0305-4470/39/32/S20",
"journal_ref": "J.Phys. A39 (2006) 10207-10228",
"title": "Non-Hermitian Quantum Mechanics of Non-diagonalizable Hamiltonians: puzzles with self-orthogonal states",
"url": "https://arxiv.org/abs/quant-ph/0602207"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "019253c9-8edf-476c-b904-45488590d450",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}