Znojil, Miloslav Solvable non-Hermitian discrete square well with closed-form physical inner product. (English) Zbl 1315.81044 J. Phys. A, Math. Theor. 47, No. 43, Article ID 435302, 18 p. (2014). From the author’s 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 \(\Theta\) which becomes equal to the most common Dirac’s metric \(\Theta^{\text{(Dirac)}}=I\) in the conventional textbook Hermitian-Hamiltonian limit. This metric is constructed in closed form at all \(N=2,3,\dots \). Reviewer: Daniel Cárdenas-Morales (Jaén) Cited in 5 Documents MSC: 81Q12 Nonselfadjoint operator theory in quantum theory including creation and destruction operators 81Q80 Special quantum systems, such as solvable systems 41A50 Best approximation, Chebyshev systems 39A12 Discrete version of topics in analysis Keywords:exactly solvable quantum models; discrete lattice; non-Hermitian boundary conditions; physical inner product PDFBibTeX XMLCite \textit{M. Znojil}, J. Phys. A, Math. Theor. 47, No. 43, Article ID 435302, 18 p. (2014; Zbl 1315.81044) Full Text: DOI arXiv