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Wavelet-like orthonormal bases for the lowest Landau level. (English) Zbl 0867.42018

Summary: 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 \(L^2(\mathbb{R})\). We discuss in detail two relevant examples coming from wavelet analysis, the Haar and the Littlewood-Paley bases.

MSC:

42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
82D05 Statistical mechanics of gases
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