The main purpose of the present paper is to investigate the semiclassical asymptotics of eigenvalues for the Dirac operator with magnetic fields. In the case of the Schrodinger operator with magnetic field, this problem was recently solved by Matsumoto. We show that the nth positive eigenvalue of th
Semiclassical Asymptotics of Eigenvalues for Schrödinger Operators with Magnetic Fields
✍ Scribed by H. Matsumoto
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 663 KB
- Volume
- 129
- Category
- Article
- ISSN
- 0022-1236
No coin nor oath required. For personal study only.
✦ Synopsis
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 we also discuss them. it 1995 Academic Press. Inc.
📜 SIMILAR VOLUMES
## Abstract For semiclassical Schrödinger 2×2–matrix operators, the symbol of which has crossing eigenvalues, we investigate the semiclassical Mourre theory to derive bounds __O__(__h__^−1^) (__h__ being the semiclassical parameter) for the boundary values of the resolvent, viewed as bounded operat
## Abstract We study the existence and completeness of the wave operators __W~ω~(A(b),‐Δ__) for general Schrodinger operators of the form equation image is a magnetic potential.
## Abstract We study the eigenvalues of Schrödinger type operators __T__ + __λV__ and their asymptotic behavior in the small coupling limit __λ__ → 0, in the case where the symbol of the kinetic energy, __T__ (__p__), strongly degenerates on a non‐trivial manifold of codimension one (© 2010 WILEY‐V
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
Spectrum of the second-order differential operator with periodic point interactions in L 2 R is investigated. Classes of unitary equivalent operators of this type are described. Spectral asymptotics for the whole family of periodic operators are calculated. It is proven that the first several terms