Dynamical noncommutative quantum mechanics

TL;DR

This paper explores quantum systems in dynamical noncommutative spaces with position-dependent commutation relations, revealing stringlike objects and a fundamental energy scale, and proposes using the Stark effect to distinguish dynamical from non-dynamical noncommutativity.

Contribution

It introduces the concept of dynamical noncommutative spaces with position-dependent relations and analyzes their physical implications, including a new fundamental energy scale.

Findings

Stringlike fundamental objects in dynamical noncommutative spaces

Existence of a fundamental energy scale $rac{ au ext{hbar}^2}{m}$

Stark effect as a probe for dynamical noncommutativity

Abstract

We study some basic and interesting quantum mechanical systems in dynamical noncommutative spaces in which the space- space commutation relations are position dependent. It is observed that the fundamental objects in the dynamical noncommutative space introduced here are stringlike. We show that the Stark effect can be employed to determine whether the noncommutativity of space is dynamical or non-dynamical. It appears that unlike non-dynamical case there is a fundamental energy $\dfrac{\tau\hbar^{2}}{m}$ in this dynamical space.}