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 -