Quantum uncertainty relation saturated by the eigenstates of the harmonic oscillator
Quantum uncertainty relation saturated by the eigenstates of the harmonic oscillator
We re-derive the Schr\"{o}dinger-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 …