Solution of the three-body problem at zero energy by the boundary condition method
Teoretičeskaâ i matematičeskaâ fizika, Tome 23 (1975) no. 1, pp. 78-93
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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.
@article{TMF_1975_23_1_a7,
author = {N. N. Beloozerov},
title = {Solution of the three-body problem at zero energy by the boundary condition method},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {78--93},
publisher = {mathdoc},
volume = {23},
number = {1},
year = {1975},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1975_23_1_a7/}
}
TY - JOUR AU - N. N. Beloozerov TI - Solution of the three-body problem at zero energy by the boundary condition method JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1975 SP - 78 EP - 93 VL - 23 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_1975_23_1_a7/ LA - ru ID - TMF_1975_23_1_a7 ER -
N. N. Beloozerov. Solution of the three-body problem at zero energy by the boundary condition method. Teoretičeskaâ i matematičeskaâ fizika, Tome 23 (1975) no. 1, pp. 78-93. http://geodesic.mathdoc.fr/item/TMF_1975_23_1_a7/