par Mandilara, Aikaterini ;Cerf, Nicolas
Référence Physical review. A, Atomic, Molecular, and Optical Physics, 86, 3, 030102
Publication Publié, 2012-09
Article révisé par les pairs
Résumé : We rederive the Schrödinger-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. © 2012 American Physical Society.