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Asymptotic behavior of eigenfunctions of the three-particle Schrödinger operator. II: Charged one-dimensional particles. (English. Russian original) Zbl 1219.81235

St. Petersbg. Math. J. 22, No. 3, 379-392 (2011); translation from Algebra Anal. 2010, No. 3, 60-79 (2010).
Summary: A system of three one-dimensional quantum particles with Coulomb pairwise interaction is treated. A scattered plane wave type asymptotic description at infinity in the configuration space of generalized eigenfunctions is obtained. Though remaining at a heuristic level, the constructions of the paper may serve as a basis for rigorous proofs of the results.
For Part I see [the autors, in: T. Suslina et al., Spectral theory of differential operators. M. Sh. Birman 80th anniversary collection. Providence, RI: American Mathematical Society (AMS). Translations. Series 2. American Mathematical Society 225; Advances in the Mathematical Sciences 62, 55–71 (2008; Zbl 1160.81476)].

MSC:

81U10 \(n\)-body potential quantum scattering theory

Citations:

Zbl 1160.81476
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References:

[1] V. S. Buslaev and S. B. Levin, Asymptotic behavior of the eigenfunctions of the many-particle Schrödinger operator. I. One-dimensional particles, Spectral theory of differential operators, Amer. Math. Soc. Transl. Ser. 2, vol. 225, Amer. Math. Soc., Providence, RI, 2008, pp. 55 – 71. · Zbl 1160.81476
[2] V. S. Buslaev, S. B. Levin, P. Neittaannmäki, and T. Ojala, 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, arXiv:0909.4529v1 [math-ph], (2009). · Zbl 1193.81111
[3] L. D. Faddeev, Mathematical questions in the quantum theory of scattering for a system of three particles, Trudy Mat. Inst. Steklov. 69 (1963), 122 (Russian). L. D. Faddeev, Mathematical aspects of the three-body problem in the quantum scattering theory, Translated from the Russian by Ch. Gutfreund. Translation edited by L. Meroz, Israel Program for Scientific Translations Jerusalem; Daniel Davey & Co., Inc., New York, 1965.
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