New mathematics for the nonadditive Tsallis’ scenario

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.

Teaching strategy for introducing beginners to Coherent States

“…An extremely short, illustrative but by no means exhaustive, is that of Refs. [1][2][3][4][5][6] and references therein. A coherent state is that quantum state that shows a dynamic closely resembling that of a classical harmonic oscillator (HO).…”

“…In order to provide the reader with an alleviated learning job, we will use a compact closed expression for CS, recently used in [3], that can be easily handled by beginners and nonexperts in Glauber's theory.…”

Useful Dual Functional of Entropic Information Measures

“…In our classification efforts we were aided by using the pure state entropy advanced and utilized in References [ 9 , 10 , 11 , 12 , 13 ]. Our pure states are the coherent ones of the HO (CHO), taking advantage of the closed analytical representation of them advanced in References [ 18 , 19 ]. They are unique in the sense of possessing minimum Heisenberg uncertainty.…”

“…Reference [ 18 ] introduced for the first time ever an analytic, compact expression for coherent states, that was a posteriori extensively discussed in Reference [ 19 ]. the new coherent states’ compact expression advantageously replaces the customary Glauber’s infinite expansion in terms of the harmonic oscillator eigenstates .…”

“…We see then that our ignorance measure [ 4 ] exhibits adequate credentials to be seriously considered. the wave function (wf) we will be interested in here is that advanced in References [ 18 , 19 ], which compactly describes in simple analytic terms the coherent states of the harmonic oscillator (HO), advantageously replacing the usual, cumbersome infinite sum.…”