GLOBAL MINIMUM PRINCIPLE FOR ONE-DIMENSIONAL INVERSE SCATTERING WITH BOUND-STATES

Recently, a global minimum principle has been proposed for the one-dim ensional inverse scattering problem for the Schrodinger equation on th e real line and in the absence of bound states. In this letter, this r estriction is removed and it is shown that the minimum principle, suit ably generalized, holds for potentials with bound states. For each coo rdinate x, a functional of the reflection coefficient and a variationa l wavefield is defined. It is shown that the minimum of this functiona l yields the negative of the line integral of the potential on the int erval {-infinity, x}.