 Solution

ID: past-exam-of-the-physics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2024/paper-1/section-b/9/d/solution

p (x) = \frac{2}{L} sin^{2} \frac{2 π x}{L} (0 \leq x \leq L),

and zero outside. It has zeros at

0, L /2, L

and equal maxima

2/ L

L /4, 3 L /4

. The two lobes have equal integrated probability. The vertical axis is a density with units of inverse length, not a dimensionless probability at a point.

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