Observables of complex PT-symmetric “Shifted” potentials

Abstract

We study complex PT-symmetric potentials, with real eigenvalues, co responding to a complex coordinate shift (equation found) of a real even potential. In this case, the rules to achieve a coherent quantum mechanics are known. They allow the calculation of observables, which are found to be independent on c. This result is illustrated by few analytical or semi analytical examples. On the other hand, trying to test this property numerically faces problems linked to the difficulty of finding the proper solutions of the Schrödinger equation. In particular, the large distance behaviour of the wave functions generates instabilities. As an example, we have studied the (equation found) potential.