Formally applying when the algebra of a group of operators is non-trivial, this idea derived from the Schwarz inequality on a Hilbert space of eigenstates can be seen to hold for components of angular momentum by the classical angular momentum commutators; that's because a version of it holds for any non-commuting observables.
One extension of this idea can be derived by considering any observable that does not vary with time alone and using Ehrenfest's theorem; that relation applies to energy and time. Formally applying when the algebra of a group of operators is non-trivial, this idea derived from the Schwarz inequality on a Hilbert space of eigenstates can be seen to hold for components of angular momentum by the classical angular momentum commutators; that's because a version of it holds for any non-commuting observables. For 10 points, name this fundamental tenet of quantum mechanics the most familiar form of which states that the standard errors in measurements of position and momentum must be at least h-bar over two.
One extension of this idea can be derived by considering any observable that does not vary with time alone and using Ehrenfest's theorem; that relation applies to energy and time.
the Heisenberg {uncertainty principle} [or {uncertainty relation}]