  We present the uncertainty relation for the characteristic functions (ChUR)
of the quantum mechanical position and momentum probability distributions. This
inequality is more general than the Heisenberg Uncertainty Relation, and is
saturated in two extremal cases for wavefunctions described by periodic Dirac
combs. We further discuss a broad spectrum of applications of the ChUR, in
particular, we constrain quantum optical measurements involving general
detection apertures and provide the uncertainty relation that is relevant for
Loop Quantum Cosmology. A method to measure the characteristic function
directly using an auxiliary qubit is also briefly discussed.
