= Oscillator uncertainty and allocation of classical energy
{title2=$\Delta x_n^2=(n+1/2)\hbar/(m\omega)$}
For a one-dimensional oscillator eigenstate, <parity> gives $\langle x\rangle=0$ and its coordinate <variance> is the displayed expression. A classical oscillator with that coordinate <energy> has turning amplitude $A=\sqrt{2E_x/(m\omega^2)}$, so $\Delta x=A/\sqrt2$. In several dimensions the total <energy> does not specify a given coordinate's classical amplitude until its <energy> allocation is fixed. <zero-point energies> in the other quantum coordinates must not silently be assigned to that one classical mode.
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