A new time-dependent quantum theory based on Tsallis' distribution

Abstract

In this paper, inspired by Tsallis' probability distribution based on a $q$-deformed Boltzmann factor, we stipulate a new $q$-deformed quantum dynamics by applying the inverse Wick rotation ${\hat{I}}^2\to it$ to the Tsallis-deformed Boltzmann factor. We obtain a new time-dependent $q$-deformed Schrödinger equation. The free time-evolution of a Gaussian wave packet and that induced by an harmonic interaction are studied within this $q$-deformed quantum mechanical framework.

11 pages, 3 figures