A family of complex potentials with real spectrum

Abstract

We consider a two-parameter non-Hermitian quantum mechanical Hamiltonian operator that is invariant under the combined effects of parity and time reversal transformations. Numerical investigation shows that for some values of the potential parameters the Hamiltonian operator supports real eigenvalues and localized eigenfunctions. In contrast with other parity times time reversal symmetric models which require special integration paths in the complex plane, our model is integrable along a line parallel to the real axis.