 Solution

ID: past-exam-of-the-relativity-course-of-the-university-of-cambridge/2022/section-b/5/b/solution

E = 0

in part (a), substitute the two conserved quantities, and multiply the normalization by

f

c^{2} k^{2} - \overset{r}{˙}^{2} - f \frac{h ^{2}}{r ^{2}} = 0.

\frac{1}{2} \overset{r}{˙}^{2} + V_{eff} (r) = \frac{1}{2} c^{2} k^{2}, V_{eff} (r) = \frac{h ^{2}}{2 r ^{2}} (1 - \frac{2 μ}{r}) .

Only radii where the total radial energy is at least this effective potential are accessible.

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