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A generalization of the radiation condition of Sommerfeld for \(N\)-body Schrödinger operators. (English) Zbl 0804.35113
The author proposes a new formulation of the radiation condition for the \(N\)-body problem. Because of the presence of many channels, the resolvent of the \(N\)-body Schrödinger operator does not behave like that of the Laplacian. The proof of the main theorem consists in introducing the algebraic framework which is inspired by the classical idea of integration by parts and the algebra of pseudo-differential operators.
Reviewer: L.-I.Anita (Iaşi)
35Q40 PDEs in connection with quantum mechanics
35A27 Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs
35J10 Schrödinger operator, Schrödinger equation
81V70 Many-body theory; quantum Hall effect
Full Text: Numdam EuDML