Equilibrium and eigenfunctions estimates in the semi-classical regime

Details Equilibrium and eigenfunctions estimates in the semi-classical regime Equilibrium and eigenfunctions estimates in the semi-classical regime

2006-05-24

arxiv.org/abs/math/0605637v1

Mathematics

Analysis of PDEs

13 pages, 1 figure, perhaps to be revised

Scientific paper

We establish eigenfunctions estimates, in the semi-classical regime, for critical energy levels associated to an isolated singularity. For Schr\"odinger operators, the asymptotic repartition of eigenvectors is the same as in the regular case, excepted in dimension 1 where a concentration at the critical point occurs. This principle extends to pseudo-differential operators and the limit measure is the Liouville measure as long as the singularity remains integrable.

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