= Infinite-well ground-state uncertainty product
{title2=$\Delta x\Delta p=\hbar\sqrt{\pi^2/12-1/2}$}
For the normalized <ground state> $\sqrt{2/L}\sin(\pi x/L)$ on $0<x<L$, direct position <integrals> give $\Delta x^2=L^2(1/12-1/(2\pi^2))$. The kinetic <momentum> second moment gives $\Delta p^2=\pi^2\hbar^2/L^2$. Their product is about $0.568\hbar$, strictly above the <Heisenberg uncertainty principle> bound. Infinite walls do not make this non-Gaussian state a minimum-uncertainty wave packet.
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