Quantum Caustics for Systems with Quadratic Lagrangians

TL;DR

This paper investigates caustics in classical and quantum systems with quadratic Lagrangians, deriving a transition amplitude formula and examining implications for quantum experiments and theoretical hypotheses.

Contribution

It provides a closed-form expression for transition amplitudes on caustics and challenges existing hypotheses about stationary points in quantum mechanics.

Findings

Derived a closed-form transition amplitude on caustics

Analyzed implications in Gaussian slit experiments

Questioned Jevicki's correspondence hypothesis

Abstract

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.