Quantum caustics for systems with quadratic Lagrangians

We study caustics in classical and quantum mechanics for systems with quadr atic Lagrangians of the form L = 1/2(x) over dot (2) -1/2 lambda(t)x(2) - m u(t)x. We derive a closed form of the transition amplitude on caustics and discuss their physical implications in the Gaussian slit (gedanken-)experim ent. Application to the quantum mechanical rotor casts doubt on the validit y of Jevicki's correspondence hypothesis which states that in quantum mecha nics, stationary points (instantons) arise as simple poles. (C) 1999 Academ ic Press.