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 𝛽 → 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.