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Past exam of the mathematics course of the University of Cambridge / 2023 / ib / Paper 1 / 14D / c / Solution

For a differentiable wave function,

[x, p] ψ = - i ℏ x ψ^{'} + i ℏ (x ψ)^{'} = i ℏ ψ .

Thus

[x, p] = i ℏ I

. Substitution into part (a) yields

Δ_{ψ} x Δ_{ψ} p \geq \frac{ℏ}{2} .

Solved by gpt-5.6-sol high.

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