Microlocal properties of sheaves and complex WKB

TL;DR

This paper uses sheaf theory to analyze the analytic continuation of solutions to a Laplace-transformed Schrödinger equation with a small parameter, providing partial proof of the Stokes phenomenon in WKB asymptotics as predicted by Voros.

Contribution

It introduces a sheaf-theoretic approach to justify the analytic continuation and describes the Stokes phenomenon in WKB analysis, advancing the mathematical understanding of quantum asymptotics.

Findings

Partial proof of Voros' prediction of the Stokes phenomenon

Sheaf theory applied to Laplace-transformed Schrödinger equations

Clarification of microlocal properties in WKB asymptotics

Abstract

Kashiwara-Schapira style sheaf theory is used to justify analytic continuability of solutions of a Laplace transformed Schroedinger equation with a small parameter. This partially proves the description of the Stokes phenomenon for WKB asymptotics predicted by Voros in 1983.