New mathematics for the non additive Tsallis' scenario

FERRI, G.L.; ROCCA, M.C.; PLASTINO, A.; PENNINI, F.

INTERNATIONAL JOURNAL OF MODERN PHYSICS B

WORLD SCIENTIFIC PUBL CO PTE LTD

Lugar: London, UK; Año: 2017 vol. 31 p. 175051 - 175070

0217-9792

In this paper, we investigate quantum uncertainties in a Tsallis? nonadditive scenario. To such an end we appeal to (Formula presented.)-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 (Formula presented.), (ii) mean values for some functions of space an momenta and (iii) concomitant quantum uncertainties. The latter are then compared to the usual ones.