Uniform asymptotic expansions of the solutions of Stueckelberg's system with turning points (Q1807455)

The uniform asymptotics of a pair of coupled inhomogeneous Schrödinger equations associated with the inelastic collision of two atoms is examined by considering the equivalent differential equation of the fourth order. This equation has two turning points and methods adumbrated by \textit{F. W. J. Olver} [Philos. Trans. Roy. Soc. London, Ser. A 278, 137-174 (1975; Zbl 0301.34072)] and further developed by the author [Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 186, 172-179 (1990; Zbl 0734.34054)]. The case involving a potential barrier is treated in detail.