Complex potentials and the inverse problem

Abstract EN

The occurrence of complex potentials with real eigenvalues has implications concerning the inverse problem, i.e.

the determination of a potential from its spectrum.

First, any complex potential with real eigenvalues has at least one equivalent local potential.

Secondly, a real spectrum does not necessarily corresponds to a local real potential.

A basic ambiguity arises from the possibility the spectrum to be generated by a complex potential.

The purpose of this work is to discuss several aspects of this problem.