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Journal of Mathematical Physics

On the definition of scattering subspaces in nonrelativistic quantum mechanics

John D. Dollard

Published Feb 1, 1977• 7 citations
Publisher

Abstract

A physically motivated definition of scattering subspaces is given for problems in nonrelativistic quantum mechanics. The definition is more stringent than earlier similar definitions. It is applicable to potential scattering and to n-body problems.
DOI
10.1063/1.523260

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The field theoretical formulation of quantum mechanics is used to consider the nonrelativistic multichannel scat~i~ng theory. With the help of appropriately constructed time dependent creation operators, Hilbert vectors are formed whose limits in time can be defined as multiehanne) scattering states in the usual sense. The existence of these states is proved under certain assumptions for the potential, by showing the convergence of the above mentioned operators. The commutation relations for the limits of these operators are given.