Geodesic
Asymptotic behavior of eigenfunctions of the three-particle Schr\"odinger operator.~II. Charged one-dimensional particles
Algebra i analiz, Tome 22 (2010) no. 3, pp. 60-79.

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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.
Keywords: quantum scattering, three-particle scattering, Coulomb interaction, one-dimensional particles. 
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V. S. Buslaev; S. B. Levin. Asymptotic behavior of eigenfunctions of the three-particle Schr\"odinger operator.~II. Charged one-dimensional particles. Algebra i analiz, Tome 22 (2010) no. 3, pp. 60-79. http://geodesic.mathdoc.fr/item/AA_2010_22_3_a3/

[1] Buslaev V. S., Levin S. B., “Asymptotic behavior of the eigenfunctions of the many-particle Schrödinger operator. I. One-dimensional particles”, Spectral Theory of Differential Operators, Amer. Math. Soc. Transl. (2), 225, Amer. Math. Soc., Providence, RI, 2008, 55–71 | MR | Zbl

[2] Buslaev V. S., Levin S. B., 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, 2009, arXiv: 0909.4529v1[math-ph]

[3] Faddeev L. D., Matematicheskie voprosy kvantovoi teorii rasseyaniya dlya sistemy trekh chastits, Tr. Mat. in-ta AN SSSR, 69, 1963 | MR | Zbl