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Numerical construction of the continuous spectrum Eigenfunctions of the three body Schrödinger operator: Three particles on the axis with short-range pair potentials

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Abstract

Based on a new method of the numerical construction of the three-body Schrödinger operator continuous spectrum eigenfunctions an analysis of the solutions of the problem of three identical particles on the axis with quickly decreasing repulsive pair potentials is offered. The initial problem is reduced to solving an inhomogeneous boundary problem for an elliptical partial differential equation in a twodimensional domain as a circle with radiation boundary conditions, with a ray approximation of the solution with diffraction corrections, contributing to a smoothness of a solution sought, being used. The approach offered allows a natural generalization for a case of slowly decreasing potentials of the Coulomb type and higher configuration space dimensions.

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Authors and Affiliations

  1. Department of Mathematical and Computational Physics, Institute of Physics, St. Petersburg State University, St. Petersburg, Russia

    V. S. Buslaev, Ya. Yu. Koptelov, S. B. Levin & D. A. Strygina

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  1. V. S. Buslaev
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  2. Ya. Yu. Koptelov
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  3. S. B. Levin
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  4. D. A. Strygina
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Correspondence to S. B. Levin.

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Original Russian Text © V.S. Buslaev, Ya.Yu. Koptelov, S.B. Levin, D.A. Strygina, 2013, published in Yadernaya Fizika, 2013, Vol. 76, No. 2, pp. 236–246.

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Buslaev, V.S., Koptelov, Y.Y., Levin, S.B. et al. Numerical construction of the continuous spectrum Eigenfunctions of the three body Schrödinger operator: Three particles on the axis with short-range pair potentials. Phys. Atom. Nuclei 76, 208–218 (2013). https://doi.org/10.1134/S1063778813010043

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  • DOI: https://doi.org/10.1134/S1063778813010043

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