Applications of Wavelets to Quantum Mechanics: a Pedagogical Example

Abstract

We discuss in many details two quantum mechanical models of planar electrons which are very much related to the Fractional Quantum Hall Effect. In particular, we discuss the localization properties of the trial ground states of the models starting from considerations on the numerical results on the energy. We conclude that wavelet theory can be conveniently used in the description of the system. Finally we suggest applications of our results to the Fractional Quantum Hall Effect.

23 pages, Latex file, Accepted by Journal of Physics A

Cited by in corpus (6)

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• Multi-Resolution Analysis and Fractional Quantum Hall Effect: an Equivalence Result
• Relations between multi-resolution analysis and quantum mechanics
• Wavelets and Quantum Algebras
• Quasi-Continuous Symmetries of Non-Lie Type
• Gabor-like systems in $L^2({\mathbf{R}}^d)$ and extensions to wavelets