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Second moments of a complex Gaussian wave packet

For a normalized wavefunction

ψ (x) = A e^{- B x^{2}}

with

Re B > 0

,

⟨ x^{2} ⟩ = \frac{1}{4 Re B}, ⟨ p^{2} ⟩ = \frac{ℏ ^{2} ∣ B ∣ ^{2}}{Re B} .

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