Keplerian trajectories and simple global Airy-type asymptotic solution of the scattering problem for the Schroedinger equation with a repulsive Coulomb potential.

Joint work with S.B.Levin (St. Petersburg State University), A.A.Tolchennikov (Ishlinsky Institute for Problems in Mechanics RAS).
The exact solution of the scattering problem for the Schroedinger equation with a repulsive Coulomb potential in the form of a degenerate hypergeometric is well known (see the book S. P. Merkuryev, L.D. Faddeev, Quantum scattering theory for systems of several particles, Moscow: Nauka, 1998; Springer 1993).
With the help of recently developed approaches, we construct simple explicit semiclassical asymptotic formulas for solving this problem in the form of the Airy function of a complex argument. The answer relies on a suitable Lagrangian manifold woven from well-known Keplerian trajectories.
The work was supported by the Russian Science Foundation under grant 21-71-3001.