Abstract
A new exactly solvable cryptohermitian quantum chain model is proposed and analyzed. Its discrete-square-well-like Hamiltonian with the real spectrum possesses a manifestly non-Hermitian form. It is only made self-adjoint by the constructive transition to an ad hoc Hilbert space. Such a space (i.e., the closed form of its inner product, i.e., the “metric” Θ) varies with an N-plet of optional parameters. The simplicity of our model enables one to obtain the complete family of these physics-determining metrics Θ in a user-friendly band-matrix closed form.
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