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

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 T which becomes equal to the most common Dirac's metric Theta((Dirac)) = I in the conventional textbook Hermitian-Hamiltonian limit. This metric is constructed in closed form at all N = 2, 3, ....