Abstract
We study localization properties of low-lying eigenfunctions of magnetic Schrödinger operators ( − i ∇ − A ( x ) ) 2 ϕ + V ( x ) ϕ = λ ϕ , where V : Ω → R ≥ 0 is a given potential and A : Ω → R d induces a magnetic field. We extend the Filoche-Mayboroda inequality and prove a refined inequality in the magnetic setting which can predict the points where low-energy eigenfunctions are localized. This result is new even in the case of vanishing magnetic field A ≡ 0 . Numerical examples illustrate the results.
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