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- W4300883336 abstract "We consider the discrete spectrum of the two-dimensional Hamiltonian $H=H_0+V$, where $H_0$ is a Schrodinger operator with a non-constant magnetic field $B$ that depends only on one of the spatial variables, and $V$ is an electric potential that decays at infinity. We study the accumulation rate of the eigenvalues of H in the gaps of its essential spectrum. First, under some general conditions on $B$ and $V$, we introduce effective Hamiltonians that govern the main asymptotic term of the eigenvalue counting function. Further, we use the effective Hamiltonians to find the asymptotic behavior of the eigenvalues in the case where the potential V is a power-like decaying function and in the case where it is a compactly supported function, showing a semiclassical behavior of the eigenvalues in the first case and a non-semiclassical behavior in the second one. We also provide a criterion for the finiteness of the number of eigenvalues in the gaps of the essential spectrum of $H$" @default.
- W4300883336 created "2022-10-04" @default.
- W4300883336 creator A5063946230 @default.
- W4300883336 date "2015-01-20" @default.
- W4300883336 modified "2023-09-24" @default.
- W4300883336 title "Eigenvalue Asymptotics for a Schrodinger Operator with Non-Constant Magnetic Field Along One Direction" @default.
- W4300883336 doi "https://doi.org/10.48550/arxiv.1501.04939" @default.
- W4300883336 hasPublicationYear "2015" @default.
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