Pisot q-Coherent states quantization of the harmonic oscillator

Abstract

We revisit the quantized version of the harmonic oscillator obtained through a q-dependent family of coherent states. For each q, 0< q < 1, these normalized states form an overcomplete set that resolves the unity with respect to an explicit measure. We restrict our study to the case in which 1/q is a quadratic unit Pisot number: the q-deformed integers form Fibonacci-like sequences of integers. We then examine the main characteristics of the corresponding quantum oscillator: localization in the configuration and in the phase spaces, angle operator, probability distributions and related statistical features, time evolution and semi-classical phase space trajectories.

35 pages, 22 figures

References in corpus (4)

• Quantization Methods: A Guide for Physicists and Analysts
• Coherent States and Bayesian Duality
• Generalized Heisenberg Algebras and Fibonacci Series
• Semiclassical and quantum description of motion on noncommutative plane

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