 Solution

ID: past-exam-of-the-short-options-paper-of-the-physics-prelims-of-the-university-of-oxford/2019/s3/3/c/solution

Apply the position version of the Born rule to the normalized wavefunction:

Pr (0 \leq x \leq L /3) = \int_{0}^{L /3} ∣Ψ (x) ∣^{2} d x = \frac{3}{L ^{3}} [\frac{x ^{3}}{3}]_{0}^{L /3} = \frac{1}{27} ≃ 0.0370.

The result is independent of

L

because the state and the measurement interval scale together. Most position probability lies towards the right wall, since the probability density grows as

x^{2}

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