  In this manuscript we investigate quantum uncertainties in a Tsallis' non
additive scenario. To such an end we appeal to q-exponentials, that are the
cornerstone of Tsallis' theory. In this respect, it is found that some new
mathematics is needed and we are led to construct a set of novel special states
that are the q-exponential equivalents of the ordinary coherent states of the
harmonic oscillator. We then characterize these new Tsallis' special states by
obtaining the associated i) probability distributions for a state of momentum
$k$, ii) mean values for some functions of space an momenta, and iii)
concomitant quantum uncertainties. The latter are then compared to the usual
ones.
