Position uncertainty ($\Delta x=\sqrt{⟨x^2⟩-⟨x{⟩}^2}$)

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 $\Delta x=\sqrt{\hslash /(2m\omega )}$ independently of its mean position; translating the state changes the mean without changing this variance.