# When the 3D Magnetic Laplacian Meets a Curved Edge in the Semiclassical Limit

@article{Popoff2013WhenT3,
title={When the 3D Magnetic Laplacian Meets a Curved Edge in the Semiclassical Limit},
author={Nicolas Popoff and Nicolas Raymond},
journal={SIAM J. Math. Analysis},
year={2013},
volume={45},
pages={2354-2395}
}
We study the magnetic Laplacian in the case when the Neumann boundary contains an edge. We provide complete asymptotic expansions in powers of $h^{1/4}$ of the low lying eigenpairs in the semiclassical limit $h\to 0$. In order to get our main result we establish a general method based on a normal form procedure, microlocal arguments, the Feshbach--Grushin reduction, and the Born--Oppenheimer approximation.

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