q-Deformed Dynamics and Virial Theorem

TL;DR

This paper explores the q-deformed Virial theorem within quantum mechanics, demonstrating improved dynamical properties and deviations from the classical uncertainty principle in specific states.

Contribution

It introduces a self-consistent framework for the q-deformed Virial theorem and analyzes its implications on uncertainty relations.

Findings

q-deformed quantum mechanics shows better dynamical properties

The framework is self-consistent for zero potential

Uncertainty relations deviate from Heisenberg in selfadjoint states

Abstract

In the framework of the q-deformed Heisenberg algebra the investigation of $q$-deformation of Virial theorem explores that q-deformed quantum mechanics possesses better dynamical property. It is clarified that in the case of the zero potential the theoretical framework for the q-deformed Virial theorem is self-consistent. In the selfadjoint states the q-deformed uncertainty relation essentially deviates from the Heisenberg one.