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CPT-symmetric discrete square well

A new version of an elementary PT-symmetric square well quantum model is proposed in which a certain Hermiticity-violating end-point interaction leaves the spectrum real in a large domain of couplings $λ\in (-1,1)$. Within this interval we employ the usual coupling-independent operator P of parity and construct, in a systematic Runge-Kutta discrete approximation, a coupling-dependent operator of charge C which enables us to classify our P-asymmetric model as CPT-symmetric or, equivalently, hiddenly Hermitian alias cryptohermitian.