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 TMF, 1975, Volume 23, Number 1, Pages 78–93 (Mi tmf3787)

Solution of the three-body problem at zero energy by the boundary condition method

N. N. Beloozerov

Abstract: System of three identical spinless bosons interacting by means of two-particle potentials of the finite range is considered. The Schrödinger equation is reduced to the problem with boundary conditions, with the aid of the assumption that the logarithmic derivative of the wave function on the potential surface does not depend on the third particle position outside the six-dimensional sphere with the radius $R$ in configuration space. In this region the ratio $r_0/R$ is a small parameter. In the lowest approximation with respect to this parameter the sequence of the boundary problem solutions at zero total energy is found. It is shown that for constructing the wave function, the generalized Fourier method can be applied, the elementary solutions of which coincide with the functions obtained.

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English version:
Theoretical and Mathematical Physics, 1975, 23:1, 362–374

Bibliographic databases:

Citation: N. N. Beloozerov, “Solution of the three-body problem at zero energy by the boundary condition method”, TMF, 23:1 (1975), 78–93; Theoret. and Math. Phys., 23:1 (1975), 362–374

Citation in format AMSBIB
\Bibitem{Bel75} \by N.~N.~Beloozerov \paper Solution of the three-body problem at zero energy by the boundary condition method \jour TMF \yr 1975 \vol 23 \issue 1 \pages 78--93 \mathnet{http://mi.mathnet.ru/tmf3787} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=475449} \transl \jour Theoret. and Math. Phys. \yr 1975 \vol 23 \issue 1 \pages 362--374 \crossref{https://doi.org/10.1007/BF01038220} 

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This publication is cited in the following articles:
1. N. N. Beloozerov, “Solution of the $nd$ scattering problem at the deuteron breakup energy by the boundary condition method”, Theoret. and Math. Phys., 33:1 (1977), 877–884
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