Keplerian trajectories and effective asymptotics of some solutions of the Schrodinger equation with a repulsive Coulomb potential.

We consider the stationary Schrodinger equation with a repulsive Coulomb potential. We construct explicit global asymptotic formulas in the form of the Airy function of a complex argument based on Lagrangian manifolds woven from Keplerian trajectories for the following problems: 1) for the scattering problem and 2) for the inhomogeneous problem with a spatially localized right-hand side. In the second case the considered problem is close to the well-known problem of the asymptotics of the Green function. The results of the work were obtained jointly with S.B.Levin, A.A.Tolchennikov and are based on approaches recently developed jointly with A.Yu.Anikin, V.E.Nazaikinsky and A.V.Tsvetkova. The work is supported by the Russian Science Foundation, project 21-11-00341.