WKB constructions in bidimensional magnetic wells. (English) Zbl 1459.35297
Summary: This article establishes, in an analytic framework and in two dimensions, the first WKB constructions describing the eigenfunctions of the pure magnetic Laplacian with low energy when the magnetic field has a unique minimum that is positive and non-degenerate.
MSC:
| 35P15 | Estimates of eigenvalues in context of PDEs |
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
| 81Q20 | Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory |
| 58J70 | Invariance and symmetry properties for PDEs on manifolds |
