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Weak pseudo-Hermiticity and antilinear commutant. (English) Zbl 1060.81026

Summary: 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.

MSC:

81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)
47N50 Applications of operator theory in the physical sciences
81U15 Exactly and quasi-solvable systems arising in quantum theory
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References:

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