 Solution

ID: past-exam-of-the-quantum-theory-course-of-the-university-of-oxford/2017/1/b/i/solution

∣Ψ (x, 0) ∣^{2} = \frac{2}{a} sin^{2} \frac{π x}{a}, \int_{- \infty}^{\infty} ∣Ψ (x, 0) ∣^{2} d x = \frac{2}{a} \int_{0}^{a} sin^{2} \frac{π x}{a} d x = 1.

The exterior contributes zero. This establishes wavefunction normalization, although the spatial quantum phase means the state is not the ground energy eigenstate.

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