On uncertainty relations in noncommutative quantum mechanics

TL;DR

This paper investigates the nature of uncertainty relations in noncommutative quantum mechanics, revealing that only one of three key relations can be saturated for a given state, with detailed analysis of angular momentum eigenstates.

Contribution

It provides a detailed analysis of uncertainty relations in noncommutative quantum mechanics, highlighting limitations on their saturation and examining angular momentum eigenstates.

Findings

Only one of three uncertainty relations can be saturated per state.

Uncertainty relations behave differently in noncommutative quantum mechanics.

Angular momentum eigenstates exhibit specific uncertainty properties.

Abstract

We discuss the uncertainty relations in quantum mechanics on noncommutative plane. In particular, we show that, for a given state at most one out of three basic nontrivial uncertainty relations can be saturated. We consider also in some detail the case of angular momentum eigenstates.