Abstract
We prove the coincidence of the two definitions of the integrated density of states (IDS) for Schrödinger operators with strongly singular magnetic fields and scalar potentials: the first one using the counting function of eigenvalues of the induced operator on a bounded open set with Dirichlet boundary conditions, the second one using the spectral projections of the whole space operator. Thus we generalize a result of \[5], where the scalar potential was non-negative. Moreover, we prove the existence of IDS for the case of periodical magnetic field and scalar potential.
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