Non-Hermitian quantum mechanics of non-diagonalizable Hamiltonians

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Non-Hermitian quantum mechanics of non-diagonalizable Hamiltonians : Puzzles with self-orthogonal states. / Sokolov, A. V.; Andrianov, A. A.; Cannata, F.

In: Journal of Physics A: Mathematical and General, Vol. 39, No. 32, S20, 11.08.2006, p. 10207-10227.

Research output: Contribution to journal › Article › peer-review

Author

Sokolov, A. V. ; Andrianov, A. A. ; Cannata, F. / Non-Hermitian quantum mechanics of non-diagonalizable Hamiltonians : Puzzles with self-orthogonal states. In: Journal of Physics A: Mathematical and General. 2006 ; Vol. 39, No. 32. pp. 10207-10227.

BibTeX

@article{df62f50e722c43b2b19c8ffffbd010ea,

title = "Non-Hermitian quantum mechanics of non-diagonalizable Hamiltonians: Puzzles with self-orthogonal states",

abstract = "We consider quantum mechanics 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 a 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 a continuous spectrum are unravelled with the help of a correct resolution of identity.",

author = "Sokolov, {A. V.} and Andrianov, {A. A.} and F. Cannata",

year = "2006",

month = aug,

day = "11",

doi = "10.1088/0305-4470/39/32/S20",

language = "English",

volume = "39",

pages = "10207--10227",

journal = "Journal of Physics A: Mathematical and Theoretical",

issn = "1751-8113",

publisher = "IOP Publishing Ltd.",

number = "32",

}

RIS

TY - JOUR

T1 - Non-Hermitian quantum mechanics of non-diagonalizable Hamiltonians

T2 - Puzzles with self-orthogonal states

AU - Sokolov, A. V.

AU - Andrianov, A. A.

AU - Cannata, F.

PY - 2006/8/11

Y1 - 2006/8/11

N2 - We consider quantum mechanics 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 a 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 a continuous spectrum are unravelled with the help of a correct resolution of identity.

AB - We consider quantum mechanics 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 a 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 a continuous spectrum are unravelled with the help of a correct resolution of identity.

UR - http://www.scopus.com/inward/record.url?scp=33746700219&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/39/32/S20

DO - 10.1088/0305-4470/39/32/S20

M3 - Article

AN - SCOPUS:33746700219

VL - 39

SP - 10207

EP - 10227

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 32

M1 - S20

ER -

ID: 98658339