Properties of minimum uncertainty wavelets and their relations to the harmonic oscillator and the coherent states

Donald J. Kouri; Manos Papadakis; Ioannis Kakadiaris; David K. Hoffman

doi:10.1021/jp030686s

Properties of minimum uncertainty wavelets and their relations to the harmonic oscillator and the coherent states

Donald J. Kouri, Manos Papadakis, Ioannis Kakadiaris, David K. Hoffman

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	7318-7327
Number of pages	10
Journal	Journal of Physical Chemistry A
Volume	107
Issue number	37
DOIs	https://doi.org/10.1021/jp030686s
State	Published - Sep 18 2003

ASJC Scopus subject areas

Physical and Theoretical Chemistry

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10.1021/jp030686s

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AB - 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.

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Properties of minimum uncertainty wavelets and their relations to the harmonic oscillator and the coherent states

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