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

TL;DR

This paper introduces a novel time-dependent quantum theory based on Tsallis' distribution, deriving a $q$-deformed Schrödinger equation and analyzing wave packet evolution within this new framework.

Contribution

It presents the first formulation of a $q$-deformed quantum dynamics derived from Tsallis' distribution using an inverse Wick rotation.

Findings

Derived a new $q$-deformed Schrödinger equation

Analyzed free Gaussian wave packet evolution

Studied harmonic oscillator within the $q$-deformed framework

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 \rightarrow i t$ to the Tsallis-deformed Boltzmann factor. We obtain a new time-dependent $q$-deformed Schr\"odinger 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.