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For a normalized wavefunction $\psi(x)=Ae^{-Bx^2}$ with $\operatorname{Re}B>0$,
$$
\langle x^2\rangle=\frac1{4\operatorname{Re}B},
\qquad
\langle p^2\rangle=\frac{\hbar^2|B|^2}{\operatorname{Re}B}.
$$


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Second moments of a complex Gaussian wave packet

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Second moments of a complex Gaussian wave packet

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