Communications in Partial Differential Equations · 2002 · 25 citations · 6 references
Natural SciencesPhysicsElectromagnetismMathematical PhysicsQuantum MechanicsEigenvalue ProblemsOperator TheoryPerturbation MethodsPerturbation TheorySpectral AnalysisSpectral TheoryDiscrete SpectrumEigenfunction ExpansionsEigenvaluesPerturbation Theory Of OperatorsSpectral Asymptotics
ABSTRACT Some spectral properties of magnetic Schrödinger and Dirac operators perturbed by long range magnetic fields are investigated. If the intensity of the field is small enough, a better location of the perturbed spectrum is given. In particular, if the unperturbed spectrum is discrete, we show that the perturbed eigenvalues are given in terms of an absolutely convergent series with respect to a magnetic parameter, from which the usual asymptotic expansion can be derived.
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