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Pseudo-Hermiticity versus \(PT\)-symmetry. II: A complete characterization of non-Hermitian Hamiltonians with a real spctrum. (English) Zbl 1060.81022

Summary: We give a necessary and sufficient condition for the reality of the spectrum of a non-Hermitian Hamiltonian admitting a complete set of biorthonormal eigenvectors. For Part I, see ibid. 43, No. 1, 205–214 (2002; Zbl 1059.81070), Part III, ibid. 43, No. 8, 3944–3951 (2002; Zbl 1061.81075)

MSC:

81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
81U15 Exactly and quasi-solvable systems arising in quantum theory
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