Solution

Past exam of the mathematics course of the University of Cambridge / 2002 / ib / Paper 2 / 18D / c / Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / ib / Paper 4 / 15A / iv / Solution

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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 Incoming links: Second moments of a complex Gaussian wave packet