Abstract
We study Schrödinger operators H(a, V): = (P − a)2 + V acting in L 2(ℝ3). We assume that the magnetic field B = rot a may be decomposed as B = B 0 + B, where B 0 is a very general field having constant direction. The perturbations B and V will be small in a certain sense in the direction of B 0, but in the orthogonal plane they may even grow for certain fields B 0. Commutator methods are used to derive spectral properties of H(a, V).
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Măntoiu, M., Pascu, M. Perturbations of Magnetic Schrödinger Operators. Letters in Mathematical Physics 54, 181–192 (2000). https://doi.org/10.1023/A:1010933504909
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DOI: https://doi.org/10.1023/A:1010933504909