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On the asymptotic behavior of eigenfunctions of the continuous spectrum at infinity in configuration space for the system of three three-dimensional like-charged quantum particles. (English. Russian original) Zbl 1380.81121

J. Math. Sci., New York 226, No. 6, 744-767 (2017); translation from Zap. Nauchn. Semin. POMI 451, 79-115 (2016).
Summary: To our knowledge there are no complete results, even not rigorously mathematically justified, related to a system of three and more quantum particles, interacting by Coulomb pair potentials, and expressed in terms of eigenfunctions. For the system of three such identical particles, asymptotic formulas describing the behavior of eigenfunctions at infinity in configuration space are suggested.

MSC:

81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
35J10 Schrödinger operator, Schrödinger equation
35P20 Asymptotic distributions of eigenvalues in context of PDEs
70F07 Three-body problems
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