Pseudo-Hermiticity versus PT-symmetry III: Equivalence of pseudo-Hermiticity and the presence of antilinear symmetries

@article{Mostafazadeh2002PseudoHermiticityVP,
title={Pseudo-Hermiticity versus PT-symmetry III: Equivalence of pseudo-Hermiticity and the presence of antilinear symmetries},
author={Ali Mostafazadeh},
journal={Journal of Mathematical Physics},
year={2002},
volume={43},
pages={3944-3951}
}
• A. Mostafazadeh
• Published 4 March 2002
• Mathematics
• Journal of Mathematical Physics
We show that a diagonalizable (non-Hermitian) Hamiltonian H is pseudo-Hermitian if and only if it has an antilinear symmetry, i.e., a symmetry generated by an invertible antilinear operator. This implies that the eigenvalues of H are real or come in complex conjugate pairs if and only if H possesses such a symmetry. In particular, the reality of the spectrum of H implies the presence of an antilinear symmetry. We further show that the spectrum of H is real if and only if there is a positive…
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