Position uncertainty
= Position uncertainty
{title2=$\Delta x=\sqrt{\langle x^2\rangle-\langle x\rangle^2}$}
The position uncertainty of a <quantum state> is the <standard deviation> of its measured <position>, provided the second moment is finite. It is computed from the <position operator> with the <Born rule>. An oscillator <coherent state> has $\Delta x=\sqrt{\hbar/(2m\omega)}$ independently of its mean <position>; translating the state changes the mean without changing this <variance>.