Pisot image-coherent states quantization of the harmonic oscillator Original Research Article

We revisit the quantized version of the harmonic oscillator obtained through a image-dependent family of coherent states. For each image, image, 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 image is a quadratic unit Pisot number, since then the image-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.