On eigenfunction expansions and scattering theory.
On resonances in mathematical scattering theory
On the completeness in three body scattering
On the derivation of the Gross-Pitaevskii equation
This article reflects in its content the talk the author gave at the XVII Congresso dellUnione Matematica Italiana, held in Milano, 8-13 September 2003. We review about some recent results on the problem of deriving the Gross-Pitaevskii equation in dimension one from the dynamics of a quantum system with a large number of identical bosons. We explain the motivations for some peculiar choices (shape of the interaction potential, scaling, initial datum). Open problems are pointed out and difficulties...
On the Scattering Matrix for N-Particle Hamiltonians