New mathematics for the non additive Tsallis' scenario

TL;DR

This paper develops new mathematical tools and special states within Tsallis' non-additive framework to analyze quantum uncertainties, extending the concept of coherent states using q-exponentials.

Contribution

It introduces a novel set of special states as q-exponential analogs of harmonic oscillator coherent states and characterizes their quantum properties.

Findings

Derived probability distributions for momentum states

Calculated mean values of functions of space and momentum

Compared quantum uncertainties with traditional cases

Abstract

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.