Quantum uncertainty relation saturated by the eigenstates of the harmonic oscillator

A. Mandilara, N. J. Cerf

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


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.

Original languageEnglish
Article number030102
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number3
Publication statusPublished - Sep 24 2012

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


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