Scaling of variables and the relation between noncommutative parameters in Noncommutative Quantum Mechanics

TL;DR

This paper explores how variable scaling affects noncommutative quantum mechanics, emphasizing the importance of effective parameters and analyzing the limited applicability of proposed proportionality relations between noncommutative parameters.

Contribution

It demonstrates that variable scaling preserves the noncommutative algebra and clarifies the conditions under which the relation between noncommutative parameters holds.

Findings

Scaling leaves the noncommutative algebra invariant

Effective parameters are the physically relevant quantities

Proposed proportionality relation has limited applicability

Abstract

We consider Noncommutative Quantum Mechanics with phase space noncommutativity. In particular, we show that a scaling of variables leaves the noncommutative algebra invariant, so that only the self-consistent effective parameters of the model are physically relevant. We also discuss the recently proposed relation of direct proportionality between the noncommutative parameters, showing that it has a limited applicability.