q-Gamow States as continuous linear functionals on analytical test functions

TL;DR

This paper introduces q-Gamow states within Tsallis' q-statistics framework, calculating their norm, mean energy, and a q-analogue of the Breit-Wigner distribution to extend resonance descriptions.

Contribution

It defines q-Gamow states as continuous linear functionals on analytical test functions, providing new mathematical tools for non-extensive statistical mechanics.

Findings

Derived the norm and mean energy of q-Gamow states

Formulated the q-analogue of the Breit-Wigner distribution

Extended resonance theory within Tsallis' q-statistics

Abstract

We define here q-Gamow states corresponding to Tsallis' q-statistics. We compute for them their norm, mean energy value an the q-analogue of the Breit-Wigner distribution (a q-Breit-Wigner).