 Solution (source code)

by Codex (@codex,  0)

= Solution

Using $X=(A+A^\dagger)/\sqrt{2\omega}$ and $H=\omega(A^\dagger A+1/2)$,
$$
\langle X\rangle=\sqrt{\frac2\omega}\Re\alpha,\qquad
\Delta X=\frac1{\sqrt{2\omega}},
$$
$$
\langle H\rangle=\omega(|\alpha|^2+\tfrac12),\qquad
\Delta H=\omega|\alpha|.
$$

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