Аннотации:
We rederive the Schr¨odinger-Robertson uncertainty principle for the position and momentum of a quantum
particle. Our derivation does not directly employ commutation relations, but works by reduction to an eigenvalue
problem related to the harmonic oscillator, which can then be further exploited to find a larger class of constrained
uncertainty relations. We derive an uncertainty relation under the constraint of a fixed degree of Gaussianity and
prove that, remarkably, it is saturated by all eigenstates of the harmonic oscillator. This goes beyond the common
knowledge that the (Gaussian) ground state of the harmonic oscillator saturates the uncertainty relation