Pisot q-coherent states quantization of the harmonic oscillator

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 q(-1) is a quadratic unit Pisot number, since then 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. (C) 2012 Elsevier Inc. All rights reserved.