# WKB eigenmode construction for analytic Toeplitz operators

## TL;DR

This paper develops a WKB-based method to construct almost eigenfunctions for Toeplitz operators with real-analytic symbols near non-degenerate wells, with exponentially small errors as the semiclassical parameter grows.

## Contribution

It introduces a novel WKB eigenfunction construction for Toeplitz operators with real-analytic symbols at non-degenerate wells, providing exponentially accurate approximations.

## Key findings

- Almost eigenfunctions follow the WKB ansatz.
- Error term is exponentially small, O(exp(-cN)).
- Applicable to Toeplitz operators with real-analytic symbols.

## Abstract

We provide almost eigenfunctions for Toeplitz operators with real-analytic symbols, at the bottom of non-degenerate wells. These almost eigenfunctions follow the WKB ansatz; the error is O(exp(--cN)), where c > 0 and N $\rightarrow$ +$\infty$ is the inverse semiclassical parameter.