Construction of maximally non-Hermitian potentials under unbroken PT−symmetry constraint

A family of discrete Schrödinger equations with imaginary and maximally non-Hermitian multiparametric potentials V(x, A, B, …) is studied. In the domain of unitarity-compatible parameters D (known as the domain of spontaneously unbroken PT−symmetry) the reality of all of the bound-state energies En(A, B, …) survives up to the maximally non-Hermitian “exceptional-point” extreme with parameters A(EP), B(EP), …. The computer-assisted proof of existence and the symbolic-manipulation localization of such a spectral-degeneracy limit are sampled showing that their complexity grows quickly with the number of parameters.