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Consider a wave packet of a particle described by the wavefunction ψ(x,0) = Axe^−(x^2/L^2), -∞ ≤  x...

Consider a wave packet of a particle described by the wavefunction ψ(x,0) = Axe^−(x^2/L^2), -∞ ≤  x ≤ ∞.

a) Draw this wavefunction, labeling the axes in terms of A and L.
b) Find the relationship between A and L that satisfies the normalization condition.
c) Calculate the approximate probability of finding the particle between positions x = −L and x = L.
d) What are 〈x〉, 〈x^2〉, and σ_x ? (Hint: use shortcuts where possible).
e) Find the minimum uncertainty in the momentum of the particle based on the results of part d and the Heisenberg uncertainty principle.

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