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The scattering problem of three one-dimensional short-range quantum particles involving bound states in pair subsystems. The coordinate asymptotics of the resolvent kernel and of the eigenfunctions of the absolutely continuous spectrum. (English. Russian original) Zbl 1455.81044

J. Math. Sci., New York 252, No. 5, 567-575 (2021); translation from Zap. Nauchn. Semin. POMI 483, 5-18 (2019).
Summary: In the present work, we consider the scattering problem of three one-dimensional quantum particles of equal mass interacting by pair finite potentials such that each pair subsystem permits a bound state. We study the limit values of the Schrödinger operator resolvent integral kernel as the spectral parameter approaches the positive semiaxis, which allows us to construct the asymptotics of eigenfunctions of the absolutely continuous spectrum.

MSC:

81U10 \(n\)-body potential quantum scattering theory
81V45 Atomic physics
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
34L20 Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators
47A10 Spectrum, resolvent
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References:

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