Calculation of the hidden symmetry operator for a -symmetric square well

It has been shown that a Hamiltonian with an unbroken symmetry also possesses a hidden symmetry that is represented by the linear operator . This symmetry operator guarantees that the Hamiltonian acts on a Hilbert space with an inner product that is both positive definite and conserved in time, thereby ensuring that the Hamiltonian can be used to define a unitary theory of quantum mechanics. In this paper it is shown how to construct the operator for the -symmetric square well using perturbative techniques.