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Buslaev, V. S.; Levin, S. B.

A system of three three-dimensional charged quantum particles: asymptotic behavior of the eigenfunctions of the continuous spectrum at infinity. (English. Russian original) Zbl 1272.81185

Funct. Anal. Appl. 46, No. 2, 147-151 (2012); translation from Funkts. Anal. Prilozh. 46, No. 2, 83-88 (2012).
Summary: To our knowledge, there are no expressions (not necessarily rigorously proved mathematically) for the eigenfunctions of a system of three or more charged quantum particles. For a system of three such identical particles, we suggest an asymptotic formula describing the behavior of eigenfunctions at infinity in the configuration space.

Cited in 4 Documents

MSC:

81U10 \(n\)-body potential quantum scattering theory
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
35P20 Asymptotic distributions of eigenvalues in context of PDEs
35P25 Scattering theory for PDEs

Keywords:

partial differential equations; mathematical physics; quantum scattering theory in the system of three charged particles
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\textit{V. S. Buslaev} and \textit{S. B. Levin}, Funct. Anal. Appl. 46, No. 2, 147--151 (2012; Zbl 1272.81185); translation from Funkts. Anal. Prilozh. 46, No. 2, 83--88 (2012)
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References:

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