New mathematics for the non additive Tsallis' scenario

Abstract

In this paper, we investigate quantum uncertainties in a Tsallis’ nonadditive In this paper, we investigate quantum uncertainties in a Tsallis’ nonadditive scenario. To such an end we appeal to q-exponentials (qEs), 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 qE equivalents of the ordinary coherent states (CS) of the harmonic oscillator (HO). We then characterize these new Tsallis’ special states by obtaining the associated (i) probability distributions (PDs) 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.