#### Vol. 6, No. 6, 2013

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From the Laplacian with variable magnetic field to the electric Laplacian in the semiclassical limit

### Nicolas Raymond

Vol. 6 (2013), No. 6, 1289–1326
##### Abstract

We consider a twisted magnetic Laplacian with Neumann condition on a smooth and bounded domain of ${ℝ}^{2}$ in the semiclassical limit $h\to 0$. Under generic assumptions, we prove that the eigenvalues admit a complete asymptotic expansion in powers of ${h}^{1∕4}$.

##### Keywords
semiclassical analysis, magnetic field, normal form
##### Mathematical Subject Classification 2010
Primary: 35J10, 35P15