The asymptotics of eigenfunctions of the absolutely continuous spectrum. The scattering problem of three one-dimensional quantum particles. (English. Russian original) Zbl 1435.81230

J. Math. Sci., New York 243, No. 5, 640-655 (2019); translation from Zap. Nauchn. Semin. POMI 471, 15-37 (2018).
Summary: In the paper the asymptotic structure of eigenfunctions of the absolutely continuous spectrum of the scattering problem is described. The case of three one-dimensional quantum particles interacting by repulsive pair potentials with a compact support is considered.


81U10 \(n\)-body potential quantum scattering theory
81U20 \(S\)-matrix theory, etc. in quantum theory
Full Text: DOI


[1] Mourre, E., Absence of singular continuous spectrum for certain self-adjoint operators, Commun. Math. Phys., 78, 391-408 (1981) · Zbl 0489.47010
[2] Perry, P.; Sigal, IM; Simon, B., Spectral analysis of N-body Schrödinger operators, Annals Math., 114, 519-567 (1981) · Zbl 0477.35069
[3] Faddeev, LD, Mathematical Aspects of the Three-Body Problem of the Quantum Scattering Theory (1965), Jerusalem: Daniel Davey and Co., Inc., Jerusalem · Zbl 0131.43504
[4] Faddeev, LD; Merkuriev, SP, Quantum Scattering Theory for Several Particle Systems (1993), Dordrecht: Kluwer, Dordrecht
[5] Baibulov, IV; Budylin, AM; Levin, SB, 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, J. Math. Sci., 238, 5, 566-590 (2019) · Zbl 1419.81009
[6] Budylin, AM; Buslaev, VS, Reflection operator and their applications to asymptotic investigations of semiclassical integral equations, Advances Soviet Math., 7, 107-157 (1991) · Zbl 0743.45003
[7] Buslaev, VS; Levin, SB, Asymptotic behavior of the eigenfunctions of the many-particle Shrödinger operator. I. One-dimentional particles, Amer. Math. Soc. Transl., 225, 2, 55-71 (2008) · Zbl 1160.81476
[8] Buslaev, VS; Levin, SB, Asymptotic behavior of the eigenfunctions of the three-body Shrödinger operator. II. One-dimensional charged particles, St. Petersburg Math. J., 22, 379-392 (2011) · Zbl 1219.81235
[9] Buslaev, VS; Levin, SB; Neittaannmäki, P.; Ojala, T., New approach to numerical computation of the eigenfunctions of the continuous spectrum of three-particle Schrödinger operator. I One-dimensional particles, short-range pair potentials, J. Phys. A: Math. Theor., 43, 285205 (2010) · Zbl 1193.81111
[10] V. S. Buslaev, S. P. Merkuriev, and S. P. Salikov, “On diffractional character of scattering in a quantum system of three one-dimensional particles,” Probl. Mat. Fiz., Leningrad. Univ., Leningrad, 9, 14-30 (1979).
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