Thurs. April 17 at 4:00pm in FRET 406

Michael Klibanov,  Department of Mathematics and Statistics, UNC Charlotte

Abstract:  This is the first solution of a long standing problem which was posed in chapter 10 of the book of K. Chadan and P. Sabatier “Inverse Problems in Quantum Scattering Theory”, Springer-Verlag, New York, 1977. 

In quantum scattering one measures only scattering cross section. This means that the modulus of the complex valued scattering wave field is measured. But phase is not measured. In the meantime the entire theory of inverse quantum scattering is based on the assumption that both modulus and phase are measured. Thus, the question was posed in the above book whether it is possible, at least in principle, to uniquely reconstruct the scattering potential if only the modulus of the scattered field is known for all frequencies. This question was addressed positively for the first time in the paper of the author published in SIAM J. Applied Mathematics, 74, #2, 392-410, 2014.