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

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

2007-07-25

arxiv.org/abs/0707.3738v2

J. Phys. A: Math. Theor. 41, 244020 (2008)

Physics

Quantum Physics

11 pages, no figures,

Scientific paper

10.1088/1751-8113/41/24/244020

A complexified von Roos Hamiltonian is considered and a Hermitian first-order intertwining differential operator is used to obtain the related position dependent mass $\eta$-weak-pseudo-Hermitian Hamiltonians. Using a Liouvillean-type change of variables, the $\eta$-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 $\eta$-weak-pseudo-Hermitian reference-Hamiltonian H(q)there is a set of exactly-solvable $\eta$-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 $\eta$-weak-pseudo-Hermitian isospectral target-Hamiltonians are obtained.

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