 Solution

ID: past-exam-of-the-physics-course-of-the-year-4-of-the-natural-sciences-course-of-the-university-of-cambridge/2012/paper-1/section-a/a1/b/solution

P (a /2 < x < a) = \frac{\int _{a /2}^{a} ( a ^{2} + x ^{2} ) d x}{\int _{0}^{a} ( a ^{2} + x ^{2} ) d x} = \frac{19 a ^{3} /24}{4 a ^{3} /3} = \frac{19}{32} .

A normalized version of the specified wavefunction is

3 (a + i x) / (2 a^{3/2})

on its support.

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