Quasi-classical approximation of monopole harmonics

TL;DR

This paper develops a quasi-classical approximation method for monopole harmonics using a generalized multidimensional WKB approach, providing explicit formulas for eigenfunctions of the Dirac monopole.

Contribution

It introduces a novel application of the generalized WKB method to magnetic Laplacians with monopoles, yielding explicit eigenfunction formulas.

Findings

Explicit quasi-classical eigenfunction formulas for Dirac monopoles

Extension of WKB method to magnetic Laplacians with monopoles

Improved understanding of monopole harmonic approximations

Abstract

Using the generalization of the multidimensional WKB method to magnetic Laplacians corresponding to monopoles, which we proposed earlier, we obtain explicit formulas for quasi-classical approximations of eigenfunctions for the Dirac monopole.