Properties of Minimum Uncertainty Wavelets and Their Relations to the Harmonic Oscillator and the Coherent States

We consider additional aspects of the recently derived “minimum uncertainty” (μ) wavelets. In particular, we show that they are fundamentally related to both the harmonic oscillator eigenstates and the canonical coherent states that play a fundamental role in quantum dynamics. In addition, we derive...

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Bibliographic Details
Published in:The journal of physical chemistry. A, Molecules, spectroscopy, kinetics, environment, & general theory Molecules, spectroscopy, kinetics, environment, & general theory, 2003-09, Vol.107 (37), p.7318-7327
Main Authors: Kouri, Donald J, Papadakis, Manos, Kakadiaris, Ioannis, Hoffman, David K
Format: Article
Language:English
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Summary:We consider additional aspects of the recently derived “minimum uncertainty” (μ) wavelets. In particular, we show that they are fundamentally related to both the harmonic oscillator eigenstates and the canonical coherent states that play a fundamental role in quantum dynamics. In addition, we derive new raising and lowering operators that apply to the μ-wavelets. Finally, we explore in some detail the senses in which the μ-wavelets form complete sets that can be used in a variety of applications in quantum dynamics.
ISSN:1089-5639
1520-5215
DOI:10.1021/jp030686s