On justification of the asymptotics of eigenfunctions of the absolutely continuous spectrum in the problem of three one-dimensional short-range quantum particles with repulsion. (English. Russian original) Zbl 1419.81009

J. Math. Sci., New York 238, No. 5, 566-590 (2019); translation from Zap. Nauchn. Semin. POMI 461, 14-51 (2017).
Summary: The present paper offers a new approach to the construction of the coordinate asymptotics of the kernel of the resolvent of the Schrödinger operator in the scattering problem of three onedimensional quantum particles with short-range pair potentials. Within the framework of this approach, the asymptotics of eigenfunctions of the absolutely continuous spectrum of the Schrödinger operator can be constructed. In the paper, the possibility of a generalization of the suggested approach to the case of the scattering problem of \(N\) particles with arbitrary masses is discussed.


81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81U05 \(2\)-body potential quantum scattering theory
47A10 Spectrum, resolvent
35B40 Asymptotic behavior of solutions to PDEs
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