Pisot -coherent states quantization of the harmonic oscillator

Abstract: We revisit the quantized version of the harmonic oscillator obtained through a -dependent family of coherent states. For each , , 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 is a quadratic unit Pisot number, since then the -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. [Copyright &y& Elsevier]