A family of complex potentials with real spectrum

Abstract

We consider a two-parameter non hermitean quantum-mechanical hamiltonian that\nis invariant under the combined effects of parity and time reversal\ntransformation. Numerical investigation shows that for some values of the\npotential parameters the hamiltonian operator supports real eigenvalues and\nlocalized eigenfunctions. In contrast with other PT symmetric models, which\nrequire special integration paths in the complex plane, our model is integrable\nalong a line parallel to the real axis.\n