Electron in a magnetic field interacting with point impurities.

We present an extensive study pertaining to the quantum-mechanical system of independent electrons in a magnetic field interacting with a finite or infinite number of point impurities (a concept that we develop below). The case where there is a single impurity is completely solved; namely, the corresponding scattering operators in two and three space dimensions are explicitly constructed and the electron spectrum is analyzed. Extension to the case where there is a finite number of impurities is straightforward. The situation is much more subtle when the set of impurities is infinite (albeit countable). We were able to derive the pertinent equations from which the spectrum and wave functions can be determined