Equilibrium and eigenfunctions estimates in the semiclassical regime. (English) Zbl 1112.81039
Summary: We establish eigenfunctions estimates, in the semiclassical regime, for critical energy levels associated to an isolated singularity. For Schrödinger operators, the asymptotic repartition of eigenvectors is the same as in the regular case, excepted in dimension one 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.
MSC:
| 81Q20 | Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory |
| 47N50 | Applications of operator theory in the physical sciences |
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
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