- Uncertainty and Entropy Properties for Coulomb and Simple Harmonic Potentials Modified by 

Uncertainty relations are the basic properties of quantum mechanics; in particular, we have the Heisenberg uncertainty principle1 for the product of the uncertainties in position and momentum

σ σ σ σx p x p x xx x p p≥ = −( ) = −( )12 2 2 2 2, , , (22.1)

22.1 Introduction .................................................................................................. 441 22.2 Heisenberg Uncertainty Relations ................................................................442