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First-order intertwining operators with position dependent mass and \(\eta\)-weak-pseudo-hermiticity generators. (English) Zbl 1139.81347

Summary: A Hermitian and an anti-Hermitian first-order intertwining operators are introduced and a class of \(\eta\)-weak-pseudo-Hermitian position-dependent mass (PDM) Hamiltonians are constructed. A corresponding reference-target \(\eta\)-weak-pseudo-Hermitian PDM-Hamiltonians’ map is suggested. Some \(\eta\)-weak-pseudo-Hermitian \(\mathcal{PT}\)-symmetric Scarf II and periodic-type models are used as illustrative examples. Energy-levels crossing and flown-away states phenomena are reported for the resulting Scarf II spectrum. Some of the corresponding \(\eta\)-weak-pseudo-Hermitian Scarf II- and periodic-type-isospectral models (\(\mathcal{PT}\)-symmetric and non- \(\mathcal{PT}\)-symmetric) are given as products of the reference-target map.

MSC:

81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
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