The time-dependent Schrödinger equation at turning points Original Research Article

The Lagrange Manifold (WKB) formalism enables the determination of the asymptotic series solution of linear hyperbolic and parabolic differential equations at turning points. Here this formalism is applied to determine the asymptotic solution of the time-dependent Schrödinger equation at turning points. We also use this approach to study some physical phenomenology associated with the time-dependent Schrödinger equation at caustics, the locus of turning points.