Properties of Minimum Uncertainty Wavelets and Their Relations to the Harmonic Oscillator and the Coherent States
Donald Jack Kouri, Manos Papadakis, Ioannis A. Kakadiaris, David K. Hoffman · The Journal of Physical Chemistry A · 2003
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.