Quantum Caustics for Systems with Quadratic Lagrangians
  We study caustics in classical and quantum mechanics for systems with quadratic Lagrangians. We derive a closed form of the transition amplitude on caustics and discuss their physical implications in the Gaussian slit (gedanken-)experiment. Application to the quantum mechanical rotor casts doubt on the validilty of Jevicki's correspondence hypothesis which states that in quantum mechanics, stationary points(instantons) arise as simple poles. 
K.Horie, H.Miyazaki, I.Tsutsui and S.Tanimura