Quantum Caustics for Systems with Quadratic Lagrangians in Multi-Dimensions

TL;DR

This paper derives a closed-form expression for quantum caustics in multi-dimensional systems with quadratic Lagrangians, extending previous work to cases with arbitrary multiplicity and illustrating the phenomena with electromagnetic field examples.

Contribution

It generalizes the analysis of quantum caustics to arbitrary multiplicity in multi-dimensional quadratic Lagrangian systems using Schulman's path-integral approach.

Findings

Derived a closed-form transition amplitude on caustics for generic multiplicity

Extended previous maximal multiplicity analysis to arbitrary multiplicity cases

Illustrated multiplicity effects with examples involving electromagnetic fields

Abstract

We study quantum caustics in $d$-dimensional systems with quadratic Lagrangians. Based on Schulman's procedure in the path-integral we derive the transition amplitude on caustics in a closed form for generic multiplicity $f$, and thereby complete the previous analysis carried out for the maximal multiplicity case $f=d$. Multiplicity dependence of the caustics phenomena is illusrated by examples of a particle interacting with external electromagnetic fields.