Asymptotic behavior of eigenfunctions of the three-particle Schrödinger operator. II. Charged one-dimensional particles
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V. S. Buslaev and S. B. Levin
Translated by: S. V. Kislyakov - St. Petersburg Math. J. 22 (2011), 379-392
- DOI: https://doi.org/10.1090/S1061-0022-2011-01147-1
- Published electronically: March 18, 2011
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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
- 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. MR 2509775, DOI 10.1090/trans2/225/04
- 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).
- 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). MR 0163695
Bibliographic 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
- Received by editor(s): December 11, 2009
- Published electronically: March 18, 2011
- Additional Notes: Supported by RFBR (grant no. 08-01-00209)
- © Copyright 2011 American Mathematical Society
- Journal: St. Petersburg Math. J. 22 (2011), 379-392
- MSC (2010): Primary 81U10
- DOI: https://doi.org/10.1090/S1061-0022-2011-01147-1
- MathSciNet review: 2729940
Dedicated: Dedicated to Ludwig Dmitrievich Faddeev on the occasion of his 75th birthday