WKB Spectral Asymptotics for a One-Dimensional Dirac Operator with a Slowly Varying Mass Profile
Abstract
We study the semiclassical spectral theory of a one-dimensional Dirac operator describing waves at the interface between topologically distinct media. We derive a modified Bohr-Sommerfeld quantization condition for the squared operator via a systematic formal WKB construction producing approximate eigenpairs. Our result differs from the standard result by the half-integer shift depending on the pseudo-spin index which allows for recovering the topologically protected zero mode. We verify our result for the solvable P\"{o}schl--Teller potential and provide numerical computations confirming the convergence of eigenvalues and eigenfunctions to their WKB approximations.
Keywords
Cite
@article{arxiv.2605.27592,
title = {WKB Spectral Asymptotics for a One-Dimensional Dirac Operator with a Slowly Varying Mass Profile},
author = {Owen Sutton and Alexander B. Watson},
journal= {arXiv preprint arXiv:2605.27592},
year = {2026}
}
Comments
27 pages, 6 figures. Owen Sutton's senior thesis at the University of Minnesota