Accardi complementarity in $\mu$-deformed quantum mechanics

TL;DR

This paper investigates the relationship between momentum and position operators in μ-deformed quantum mechanics, demonstrating they are not Accardi complementary for μ > 0 and conjecturing the same for -1/2 < μ < 0.

Contribution

It provides a proof that the operators are not Accardi complementary for μ > 0 and proposes a conjecture for the case -1/2 < μ < 0.

Findings

Momentum and position operators are not Accardi complementary for μ > 0.

Conjecture that the same non-complementarity holds for -1/2 < μ < 0.

Abstract

In this note we show that the momentum and position operators of $\mu$-deformed quantum mechanics for $\mu > 0$ are not Accardi complementary in a sense that we will define. We conjecture that this is also true if $-1/2 < \mu < 0$.