Convergent WKB Series

TL;DR

This paper demonstrates that certain exactly solvable potentials have convergent WKB series, leading to all-orders quantisation conditions that unify known cases and introduce new examples.

Contribution

It shows the convergence of WKB series for specific potentials and provides a unified framework for exact quantisation conditions, including new cases.

Findings

WKB series convergence for specific potentials

Unified description of exact quantisation conditions

Introduction of new solvable examples

Abstract

A set of simple exactly solvable potentials are shown to have convergent WKB series. The resulting all-orders quantisation conditions provide a unified description of all known cases where an exact WKB quantisation condition has been obtained by modifying the potential with Langer-style terms, together with several new examples.