Paper

Solvable non-Hermitian discrete square well with closed-form physical inner product

Published 9 October 2014 © 2014 IOP Publishing Ltd
, , Citation Miloslav Znojil 2014 J. Phys. A: Math. Theor. 47 435302 DOI 10.1088/1751-8113/47/43/435302

1751-8121/47/43/435302

Abstract

A new Hermitizable quantum model is proposed in which the bound-state energies are real and given as roots of an elementary trigonometric expression while the wave function components are expressed as superpositions of two Chebyshev polynomials. As an $N$-site lattice version of square well with complex Robin-type two-parametric boundary conditions the model is unitary with respect to the Hilbert space metric Θ which becomes equal to the most common Diracʼs metric ${{\Theta }^{({\rm Dirac})}}=I$ in the conventional textbook Hermitian–Hamiltonian limit. This metric is constructed in closed form at all $N=2,3,\ldots $.

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10.1088/1751-8113/47/43/435302