98-219 Colin de Verdi{\`e}re, Y.
La formule de Landau-Zener microlocale (131K, postscript, gzipped, uuencoded) Mar 23, 98
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Abstract. In our paper, we describe microlocal solutions to a 2-level system in dimension 1 near an avoided crossing of the eigenvalues. We derive some formula "a la Landau-Zener" with a uniform complete asymptotic expansion with respect to the gap size and the Planck constant. We apply our result to 1D-semi-classical systems of stationnary Schr{\"o}dinger equations and to time-dependent systems in the adiabatic limit.

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