 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/2017/s18/1/5/solution

R_{B} = \frac{m ^{2}}{k ^{2} ℏ ^{4}} \int e^{2 ik x} U (x) d x^{2} .

For the attractive delta this is

β^{2} / k^{2}

, the leading small-

β / k

expansion of the exact result. Physically one neglects the distortion of the incident state by repeated interaction with the potential. At low

k

the Born result can exceed one, while the exact reflection remains bounded and approaches one; it is not valid in that limit.

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