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arXiv:1111.5841

The system of three three-dimensional charged quantum particles: asymptotic behavior of the eigenfunctions of the continuous spectrum at infinity (II)

V. S. Buslaev, S. B. Levin

Published Nov 24, 2011• 0 citations
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Abstract

To our knowledge there are no complete results expressed in terms of eigenfunctions (even not strictly proved mathematically) related to the system of three or more charged quantum particles. For the system of the three such identical particles we suggest the asymptotic formula describing the behavior of eigenfunctions at infinity in configuration space.

DOI
10.48550/arxiv.1111.5841

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To our knowledge there are no complete results expressed in terms of eigenfunctions (even not strictly proved mathematically) related to the system of three or more charged quantum particles. For the system of the three such identical particles we suggest the asymptotic formula describing the behavior of eigenfunctions at infinity in configuration space.
On the leading term of asymptotics of the nnn like-charged quantum particles scattering problem solution
An ansatz describing in terms of formal asymptotic decompositions a leading term of asymptotics of the nnn three-dimensional like-charged quantum particles scattering problem solution is suggested. The description of the solution in those asymptotic configurations in which it was known earlier (for example, n=3n=3n=3), coincides with the previously known constructions \cite{BBK,z1,am92,BL2,KL}. It is shown that the Schredinger equation discrepancy for the suggested ansatz decreases faster than the potential uniformly in all angle variables at infinity in configuration space. An assumption is made about the structure of the leading term of the asymptotics of the scattering problem solution related to the nnn three-dimensional quantum particles interacting by a broad class of slowly decreasing pair potentials.