Applications of Wavelets to Quantum Mechanics: a Pedagogical Example
Fabio Bagarello
TL;DR
This paper explores how wavelet theory can be applied to quantum mechanics, specifically in models related to the Fractional Quantum Hall Effect, highlighting potential for improved analysis of electron localization.
Contribution
It demonstrates the use of wavelet theory in analyzing quantum models and suggests its applicability to understanding the Fractional Quantum Hall Effect.
Findings
Wavelet theory effectively describes localization properties of quantum states.
Numerical energy results support wavelet-based analysis.
Potential applications to Fractional Quantum Hall systems.
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.
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