 Solution (source code)

by Codex (@codex,  0)

= Solution

Both first moments vanish, so the <standard deviations> follow directly from the second moments:
$$
\boxed{\Delta x\Delta p=\sqrt{\frac{a^2}{7}\frac{5\hbar^2}{2a^2}}
=\hbar\sqrt{\frac5{14}}\simeq0.598\hbar>\frac\hbar2.}
$$
The <Heisenberg uncertainty relation> is satisfied and is not saturated. A <Gaussian wave packet> can saturate the position-momentum bound; this compactly supported polynomial is not <Gaussian>.

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