scholarly journals Limiting Absorption Principle and Equivalence of Feynman Propagators on Asymptotically Minkowski Spacetimes

2021 ◽  
Author(s):  
Kouichi Taira
Keyword(s):  
Limiting Absorption Principle

AN ABSTRACT RADIATION CONDITION AND APPLICATIONS TO N-BODY SYSTEMS

2000 ◽  
Vol 12 (05) ◽  
pp. 767-803 ◽  
Author(s):  
JACOB SCHACH MØLLER
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Stark Effect ◽  
Schrödinger Operators ◽  
Radiation Condition ◽  
Schrodinger Operators ◽  
Limiting Absorption Principle ◽  
Inhomogeneous Schrödinger Equation

In the setting of Mourre [18] we characterize the "outgoing" and "incoming" solutions, to the abstract inhomogeneous Schrödinger equation (H-E)u=v, given by the Limiting Absorption Principle. The characterization is in terms of an abstract radiation condition and as an application we give a characterization, in the framework of weighted L2-spaces, of the outgoing and incoming solutions for N-body Schrödinger operators with and without Stark effect. The abstract radiation condition translates in the application into a radiation condition considered by Isozaki in [13].

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