If two physical variables correspond to commuting Hermitian operators, they can be diagonalized simultaneously -- that is, they have a common set of eigenstates. In these eigenstates both variables ha...If two physical variables correspond to commuting Hermitian operators, they can be diagonalized simultaneously -- that is, they have a common set of eigenstates. In these eigenstates both variables have precise values at the same time, there is no “Uncertainty Principle” requiring that as we know one of them more accurately, we increasingly lose track of the other. For example, the energy and momentum of a free particle can both be specified exactly. More interesting examples will appear in the
