# A 3D-Schroedinger operator under magnetic steps

@inproceedings{Assaad2021A3O, title={A 3D-Schroedinger operator under magnetic steps}, author={W. Assaad and Emanuela L Giacomelli}, year={2021} }

. We deﬁne a Schrödinger operator on the half-space with a discontinuous magnetic ﬁeld having a piecewise-constant strength and a uniform direction. Motivated by applications in the theory of superconductivity, we study the inﬁmum of the spectrum of the operator. We further give suﬃcient conditions on the strength and the direction of the magnetic ﬁeld such that the aforementioned inﬁmum is an eigenvalue of a reduced model operator on the half-plane.

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