 Solution

ID: past-exam-of-the-short-options-paper-shared-by-prelims-and-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2018/s3/2/a/solution

Choose the overall phase so that

A

is positive. Normalization requires

1 = ∣ A ∣^{2} \int_{- a}^{a} (a^{2} - x^{2})^{2} d x = ∣ A ∣^{2} \frac{16 a ^{5}}{15} .

Therefore

A = \frac{15}{4 a ^{5/2}} .

An arbitrary constant phase multiplying this answer has no effect on any expectation value.

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