Geodesic
Magnetic Schr\"odinger operator from the point of view of noncommutative geometry
Contemporary Mathematics. Fundamental Directions, Proceedings of the Seventh International Conference on Differential and Functional-Differential Equations (Moscow, August 22–29, 2014). Part 2, Tome 59 (2016), pp. 192-200

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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. 
@article{CMFD_2016_59_a8,
     author = {A. G. Sergeev},
     title = {Magnetic {Schr\"odinger} operator from the point of view of noncommutative geometry},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {192--200},
     publisher = {mathdoc},
     volume = {59},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2016_59_a8/}
}
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A. G. Sergeev. Magnetic Schr\"odinger operator from the point of view of noncommutative geometry. Contemporary Mathematics. Fundamental Directions, Proceedings of the Seventh International Conference on Differential and Functional-Differential Equations (Moscow, August 22–29, 2014). Part 2, Tome 59 (2016), pp. 192-200. http://geodesic.mathdoc.fr/item/CMFD_2016_59_a8/