Mathematical aspects of quantum mechanical many-body problems

by Prof. Hiroshi Isozaki

Monday 1 Feb 2016, 13:30 → 14:30 Asia/Tokyo

Main Research Building 433 (RIKEN Wako)

Date: Feb 1 (Mon) Time: 13:30 - Place: Main Research bldg. 433 Speaker: Hiroshi Isozaki (University of Tsukuba) Title: Mathematical aspects of quantum mechanical many-body problems Abstract: This is an expository talk on the mathematical theory of scattering for non-relativistic quantum mechanical many-body systems. Although there is no explicit formulae for solutions to the many-body Schroedinger equation, their asymptotic behavior in time or space can be rigorously observed by a mathematical framework of scattering theory. Starting from the mathematical definition of the spectrum, bound states and scattering states are characterized by their space-time behavior. In the time-dependent picture, the scattering states break up into a sum of free waves associated with sub-systems, which gives a complete classification of scattering states by channel wave operators. In the stationary picture, for which we consider the 3-body problem, there is a complete system of generalized eigenfunctions of the 3-body Hamiltonian describing the continuous spectrum, and the S-matrix is computed from their asymptotic expansion at infinity. Only appropriate (mild) decay assumptions are required for the potentials. See more QHP seminars