Complex Potentials with Real Eigenvalues and the Inverse Problem

Abstract

International audienceThe existence of complex potentials with real eigenvalues rises twoquestions. The first one concerns the determination of the local real equivalent potentials. The second one underlines the fact that any even potential with respect to x inthe one-dimensional (D = 1) space has at least two complex partners with the samespectrum. The present paper illustrates this situation with a few examples