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Asymptotic behavior of eigenfunctions of the three-particle Schrödinger operator. II. Charged one-dimensional particles


Authors: V. S. Buslaev and S. B. Levin
Translated by: S. V. Kislyakov
Original publication: Algebra i Analiz, tom 22 (2010), nomer 3.
Journal: St. Petersburg Math. J. 22 (2011), 379-392
MSC (2010): Primary 81U10
DOI: https://doi.org/10.1090/S1061-0022-2011-01147-1
Published electronically: March 18, 2011
MathSciNet review: 2729940
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Abstract | References | Similar Articles | Additional Information

Abstract: 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.


References [Enhancements On Off] (What's this?)

  • 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. (2), vol. 225, Amer. Math. Soc., Providence, RI, 2008, pp. 55-71. MR 2509775 (2010k:81292)
  • 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).
  • 3. L. D. Faddeev, Mathematical aspects of the three-body problem in the quantum scattering theory, Trudy Mat. Inst. Steklov. 69 (1963), 122 pp.; English transl., Daniel Davey and Co., Inc., New York, 1965. MR 0163695 (29:995); MR 0221828 (36:4880)

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Additional Information

V. S. Buslaev
Affiliation: Department of Physics, St. Petersburg State University, Ul′yanovskaya 3, St. Petersburg 198504, Russia
Email: vbuslaev@gmail.com

S. B. Levin
Affiliation: Department of Physics, St. Petersburg State University, Ul′yanovskaya 3, St. Petersburg 198504, Russia

DOI: https://doi.org/10.1090/S1061-0022-2011-01147-1
Keywords: Quantum scattering, three-particle scattering, Coulomb interaction, one-dimensional particles
Received by editor(s): December 11, 2009
Published electronically: March 18, 2011
Additional Notes: Supported by RFBR (grant no. 08-01-00209)
Dedicated: Dedicated to Ludwig Dmitrievich Faddeev on the occasion of his 75th birthday
Article copyright: © Copyright 2011 American Mathematical Society

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