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ID: past-exam-of-the-chemistry-course-of-the-year-4-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-3/section-f/46/a/iv/c/solution

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Past exam of the chemistry course of the year 4 of the natural sciences course of the University of Cambridge / 2022 / Paper 3 / Section F / 46 / a / iv / C / Solution by

Codex  0 2026-10-20

For

E ≫ V_{0}

, expand the reciprocal to obtain

P (E) = 1 - \frac{V _{0}^{2}}{4 E ^{2}} sin^{2} (α a) + O [(V_{0} / E)^{3}] .

(1)

Retain the exact

α

in the bounded oscillatory factor unless a further phase expansion is controlled. Reflection is small, with an oscillatory interference correction of order

(V_{0} / E)^{2}

. The wavefunction is nearly a travelling wave throughout; its wave number inside is slightly smaller than outside, so its wavelength is slightly larger there. The reflected wave adds weak standing-wave modulation on the incident side.

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