We study the decrease of fluctuations of diagonal matrix elements of observables and of Husimi densities of quantum mechanical wave functions around their mean value upon approaching the semi-classical regime (ħ→ 0). The model studied is a spin (SU(2)) one in a classically strongly chaotic regime. We show that the fluctuations are Gaussian distributed, with a width σ^2 decreasing as the square root of Planck's constant. This is consistent with Random Matrix Theory (RMT) predictions, and

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... studies on these fluctuations. We further study the width of the probability distribution of ħ-dependent fluctuations and compare it to the Gaussian Orthogonal Ensemble (GOE) of RMT.