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Eigenvalue estimates for a three-dimensional magnetic Schr��dinger operator
- Publication Year :
- 2012
- Publisher :
- arXiv, 2012.
-
Abstract
- We consider a magnetic Schr��dinger operator $H^h=(-ih\nabla-\vec{A})^2$ with the Dirichlet boundary conditions in an open set $��\subset {\mathbb R}^3$, where $h>0$ is a small parameter. We suppose that the minimal value $b_0$ of the module $|\vec{B}|$ of the vector magnetic field $\vec{B}$ is strictly positive, and there exists a unique minimum point of $|\vec{B}|$, which is non-degenerate. The main result of the paper is upper estimates for the low-lying eigenvalues of the operator $H^h$ in the semiclassical limit. We also prove the existence of an arbitrary large number of spectral gaps in the semiclassical limit in the corresponding periodic setting.<br />20 pages
- Subjects :
- FOS: Mathematics
Spectral Theory (math.SP)
Analysis of PDEs (math.AP)
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi...........445edd07f5c525751bb6da47cc09bfe9
- Full Text :
- https://doi.org/10.48550/arxiv.1203.4021