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In this manuscript we investigate quantum uncertainties in a Tsallis' nonadditive scenario. To such an end we appeal to q-exponentials, that are thecornerstone of Tsallis' theory. In this respect, it is found that some newmathematics is needed and we are led to construct a set of novel special statesthat are the q-exponential equivalents of the ordinary coherent states of theharmonic oscillator. We then characterize these new Tsallis' special states byobtaining 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 usualones.

New mathematics for the non additive Tsallis' scenario