Magnetic Schrödinger operator from the point of view of noncommutative geometry

We give an interpretation of magnetic Schrödinger operator in terms of noncommutative geometry. In particular, spectral properties of this operator are reformulated in terms of $C^*$-algebras. Using this reformulation, one can employ the machinery of noncommutative geometry, such as Hochschild cohomology, to study the properties of magnetic Schrödinger operator. We show how this idea can be applied to the integer quantum Hall effect.