Graduate students

Given a Hermitian potential V, the scattering theory tells us how to predict observables (scattering amplitude or phase shift) in scattering experiments. In usual situations, however, we have to proceed in the opposite direction; we have to infer the operating potential from observables. This defines the inverse scattering problem ; how can we derive the potential V from observables? What is the necessary information to specify a single potential V? The current stage of our understanding of the problem is limited mainly to one-dimensional systems. Existing theories of the inverse scattering problem in three-dimensional space are based on the partial wave decomposition which reduces the space to one-dimension, and assume local potential.