THE FLOQUET METHOD FOR PT-SYMMETRIC PERIODIC POTENTIALS

Abstract

By the general theory of PT-symmetric quantum systems, their energy levels are either real or occur in complex-conjugate pairs, which implies that the secular equation must be real. However, for periodic potentials it is by no means clear that the secular equation arising in the Floquet method is indeed real, since it involves two linearly independent solutions of the Schrödinger equation. In this brief note we elucidate how that reality can be established.