Asymptotic behavior of the eigenfunctions of many-particle Schrödinger operator. I. One-dimensional particles

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

“…In [1], the case of compactly supported (or rapidly decaying) pairwise potentials was considered, and the function ψ(x, q) was studied with the following asymptotic behavior as |x|→∞:…”

“…In [1], it was explained how to use such a result for the solution of the principal problem. In [2], it was shown how the result can be used to find a solution ψ numerically if the pairwise potentials decay rapidly.…”

“…Also, in [1], the status of the problem in question within related themes was discussed, specifically, within scattering theory for 3 quantum particles, and particularly in the case of a Coulomb interaction. To summarize, the last problem remains the only one in the multiparticle scattering theory for which there is no "stationary approach," necessary for finding parameters of real physical reactions.…”

“…We confine ourselves to these short comments, supplemented by the reference to [1]. The layout of the paper is as follows.…”

“…Subdomains. Consider a finite angular neighborhood V of the ray l + 1 ; let V be bounded by rays l + and l − , the first lying inside the sector λ and the second inside λ τ 1 . We assume that these rays are symmetric with respect to l + 1 .…”