{"paper":{"title":"Non-Hermitian Quantum Mechanics of Non-diagonalizable Hamiltonians: puzzles with self-orthogonal states","license":"","headline":"","cross_cats":["cond-mat.stat-mech","hep-th","math-ph","math.MP","physics.atom-ph","physics.chem-ph"],"primary_cat":"quant-ph","authors_text":"A. A. Andrianov, A. V. Sokolov, F. Cannata","submitted_at":"2006-02-24T21:43:05Z","abstract_excerpt":"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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0602207","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}