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Limiting absorption principle for Schrödinger Hamiltonians with magnetic fields. (English) Zbl 0798.35132

The authors consider a Schrödinger operator with magnetic fields in \(\mathbb{R}^ n\) and prove that if the magnetic field decays like \(| x|^{-(1+\delta)}\) at infinity for some \(\delta>0\), and satisfies some regularity condition, then the Hamiltonian has a pure absolutely continuous spectrum on \([0,+\infty[\) with at most finitely degenerated embedded eigenvalues that can accumulate only at 0 and \(\infty\).
They prove moreover a limiting absorbtion principle for this Hamiltonian. The proof is based on a generalized version of the conjugate operator method as developed by the first author and V. Georgescu [Astérisque 210, 27-48 (1992)].
Reviewer: B.Helffer (Paris)

MSC:

35Q40 PDEs in connection with quantum mechanics
35P99 Spectral theory and eigenvalue problems for partial differential equations
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
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References:

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