CPT-symmetric discrete square well

TL;DR

This paper introduces a novel PT-symmetric quantum square well model with a Hermiticity-violating boundary interaction that maintains a real spectrum within a specific coupling range, using a systematic discrete approximation to construct a charge operator.

Contribution

It presents a new PT-symmetric square well model with a Hermiticity-violating boundary term and constructs a charge operator to establish CPT-symmetry within a certain coupling domain.

Findings

Spectrum remains real for couplings in (-1,1)

Constructed a coupling-dependent charge operator

Classified the model as CPT-symmetric or cryptohermitian

Abstract

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 $\lambda\in (-1,1)$. 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.