The uncertainty relation in a way to establish that the dispersion of two incompatible (non-interchangeable) observables can not go simultaneously to zero, which means that the observables in question can not be measured at the same time. Gamba [4] and Castoldi [5] found that the minimum bound in the Heisenberg uncertainty relation is increased by a term associated with the anticommutator of the observables involved. In this paper, it will be shown using the principle of canonical quantization and the principle of complementarity that this term corresponds to a statistical correlation derived from the Pearson correlation coefficient or more specifically from the statistical joint covariance between two observables. Additionally, we find the optimal states (states for which the minimum bound of the uncertainty relation is obtained) of operators in finite and infinite dimensional spaces, taking as an example: spin, linear moment, position, among others; all this taking into account the domains of the observables and how this intervenes in the relationship of uncertainty of Heisenberg

Theory/Pheno