Inverse Scattering Problems with the Potential Known on an Interior Subinterval

摘要

The inverse scattering problem for one-dimensional Schr¨odinger operatorson the line is considered when the potential is real valued and integrableand has a finite first moment. It is shown that the potential on the line isuniquely determined by the mixed scattering data consisting of the scatteringmatrix, known potential on a finite interval, and one nodal point on theknown interval for each eigenfunction.