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arXiv · 0707.3738

Non-Hermitian von Roos Hamiltonian's $η$-weak-pseudo-Hermiticity, isospectrality and exact solvability

Omar Mustafa·S. Habib Mazharimousavi
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Abstract

A complexified von Roos Hamiltonian is considered and a Hermitian first-order intertwining differential operator is used to obtain the related position dependent mass $η$-weak-pseudo-Hermitian Hamiltonians. Using a Liouvillean-type change of variables, the $η$-weak-pseudo-Hermitian von Roos Hamiltonians H(x) are mapped into the traditional Schrodinger Hamiltonian form H(q), where exact isospectral correspondence between H(x) and H(q) is obtained. Under a user-friendly position dependent mass settings, it is observed that for each exactly-solvable $η$-weak-pseudo-Hermitian reference-Hamiltonian H(q)there is a set of exactly-solvable $η$-weak-pseudo-Hermitian isospectral target-Hamiltonians H(x). A non-Hermitian PT-symmetric Scarf II and a non-Hermitian periodic-type PT-symmetric Samsonov-Roy potentials are used as reference models and the corresponding $η$-weak-pseudo-Hermitian isospectral target-Hamiltonians are obtained.

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Omar Mustafa, S. Habib Mazharimousavi. 2007-12-27. Non-Hermitian von Roos Hamiltonian's $η$-weak-pseudo-Hermiticity, isospectrality and exact solvability. https://doi.org/10.1088/1751-8113/41/24/244020

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