Scattering Theory - Time Independent

Roger G. Newton

J S Briggs, James M. Feagin

We consider the theory of multiple-particle fragmentation processes in the light of modern multihit position-sensitive detection. First, we give a formulation of time-independent many-body scattering theory as a direct generalization of standard textbook two-body potential scattering but in such a way as to emphasize position rather than momentum detection. Noteworthy is that classical asymptotic motion of fragments is shown to emerge from this quantum-mechanical time-independent theory and enables the definition of a classical time parameter. This in turn allows a transition to be made to a time-dependent scattering theory, even in the case where all Hamiltonians are time independent. Such a time-dependent description is the basis of the imaging theorem, which connects position detection to momentum detection.

James G. Glimm, Arthur M. Jaffe

Colston Chandler, Archie G. Gibson

Rigorous proofs are given of several theorems establishing the connection between time-dependent and time-independent multichannel scattering theory. The method of proof involves a two-Hilbert-space formulation of time-dependent multichannel theory and the theory of spectral integrals. In particular, the time-independent theory in the form proposed by Alt, Grassberger, and Sandhas is derived.