We consider Schrödinger operators with magnetic fields on a two-dimensional compact manifold or on \(\mathbf{R}^{2}\). The purpose is to study the semiclassical asymptotics of the eigenvalues by two different methods. We obtain some facts on the harmonic oscillators under uniform magnetic fields and
✦ LIBER ✦
Eigenvalue Bounds for Schrödinger Operators with a Homogeneous Magnetic Field
✍ Scribed by Rupert L. Frank; Rikard Olofsson
- Publisher
- Springer
- Year
- 2011
- Tongue
- English
- Weight
- 181 KB
- Volume
- 97
- Category
- Article
- ISSN
- 0377-9017
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📜 SIMILAR VOLUMES
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An explicit representation of lower bounds for the spectra of Schrödinger operators with magnetic fields on \(\sigma\)-compact Riemannian manifolds is given, using the positivity of the Pauli Hamiltonian. This representation is applied to show some asymptotic properties of a stochastic oscillatory i
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