Quantum Fluctuations Contribution to the Random Walk of a Single Molecule and New Estimate of the Planck Constant

It is shown, by considering the case of the harmonic oscillator, that quantum fluctuations may be the most significant contribution to the random walk of a single molecule. From this point, the controversy on the existence of a standard quantum limit (SQL) is addressed and settled on the experimental ground. Comparisons to the experimental data yet avalaible in the literature provide a new estimate of the reduced Planck constant yielding \hbar = (1.1 \pm 0.2) ~ 10^{-34} J.s.