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Weak pseudo-Hermiticity and antilinear commutant

Weak pseudo-Hermiticity and antilinear commutant

We inquire into some properties of diagonalizable pseudo-Hermitian operators, showing that their definition can be relaxed and that the pseudo-Hermiticity property is strictly connected with the existence of an antilinear symmetry. This result is then illustrated by considering the particular case of the complex Morse potential.