Wavelet-like orthonormal bases for the lowest Landau level

Abstract

As a first step in the description of a two-dimensional electron gas in a magnetic field, such as encountered in the fractional quantum Hall effect, we discuss a general procedure for constructing an orthonormal basis for the lowest Landau level, starting from an arbitrary orthonormal basis in L2(R). We discuss in detail two relevant examples coming from wavelet analysis, the Haar and the Littlewood-Paley bases.