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A plane wave in a three-body system with zero total orbital momentum. (English. Russian original) Zbl 0850.70054
Leningr. Math. J. 2, No. 4, 861-877 (1991); translation from Algebra Anal. 2, No. 4, 182-200 (1990).
Summary (Translated from the Russian): The flat wave $$\mathcal F$$ for a quantum system of three particles with fixed full orbital instant equal to zero is investigated. It is shown, that $$\mathcal F$$ is a function of two-variables, which is a solution of the appropriate eikonal equation. For $$\mathcal F$$ obvious concepts and full asymptotic decomposition are obtained at small and greater hyperradii. The authors prove the addition theorem for hyperspherical functions and three new addition theorems for some special functions.
##### MSC:
 81U10 $$n$$-body potential quantum scattering theory 35P25 Scattering theory for PDEs 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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