no. 4
The level crossing problem in semi-classical analysis I. The symmetric case
Annales de l'Institut Fourier, Volume 53 (2003) no. 4, pp. 1023-1054.

We describe a microlocal normal form for a symmetric system of pseudo-differential equations whose principal symbol is a real symmetric matrix with a generic crossing of eigenvalues. We use it in order to give a precise description of the microlocal solutions.

Nous décrivons une forme normale microlocale pour un système symétrique d'équations pseudo-différentielles dont le symbole principal est à valeurs matrices symétriques réelles ayant un croisement générique de valeurs propres. Nous utilisons cette forme normale pour décrire de façon précise les solutions mucrolocales.

DOI: 10.5802/aif.1973
Classification: 35C20,  35Q40,  35S30
Keywords: mode conversion, polarization, Born-Oppenheimer approximation, Maxwell equations, eigenvalue crossing, pseudo-differential systems, semi-classical analysis, lagrangian manifold, propagation of singularities, coherent states, symplectic spinors 
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Colin de Verdière, Yves. The level crossing problem in semi-classical analysis I. The symmetric case. Annales de l'Institut Fourier, Volume 53 (2003) no. 4, pp. 1023-1054. doi : 10.5802/aif.1973. https://aif.centre-mersenne.org/articles/10.5802/aif.1973/

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