Exploring a modified quantum dynamics 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 beta - it to the Tsallis-deformed Boltzmann factor. We obtain a new time-dependent q-deformed Schr & ouml;dinger 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.