Probing Uncertainty Relations in Non-Commutative Space

Abstract: In this paper, we compute uncertainty relations for non-commutative space and obtain a better lower bound than the standard one obtained from Heisenberg's uncertainty relation. We also derive the reverse uncertainty relation for product and sum of uncertainties of two incompatible variables for one linear and another non-linear model of the harmonic oscillator. The non-linear model in non-commutating space yields two different expressions for Schr\"odinger and Heisenberg uncertainty relation. This distinction does not arise in commutative space, and even in the linear model of non-commutative space.