Non-Hermitian Quantum Mechanics of Non-diagonalizable Hamiltonians: puzzles with self-orthogonal states
نویسندگان
چکیده
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. Submitted to: Journal of Physics A: Math. Gen. PACS numbers: 03.65.-w,03.65.Ca,03.65.Ge Non-Hermitian Quantum Mechanics 2
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