On the eigenvalues of the perturbed Schrödinger operator with irrational magnetic flow
We describe an approach to the eigenfunction problem for the perturbed Schrödinger operator \[ \left( i{ \partial \over \partial x} + 2 \pi \theta y \right)^2 - {\partial^2 \over \partial y^2} + V(x,y) \] with irrational magnetic flow and with a doubly periodic perturbation \(V(x,y) = V(x + 1, y) = V(x,y + 1)\). The approach is based on the representation of this operator as an operator in a Hilbert module over the \(C^*\)-algebra \(A_\theta\).
scientific article; zbMATH DE number 795619