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ID: past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2018/paper-2/section-a-ii/14/ii/a/solution

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Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2018 / Paper 2 / Section A(ii) / 14 / ii / a / Solution by

Codex  0 2026-10-20

Only

n = 1, 2

have energies below

6 ϵ

. Squaring the corresponding expansion coefficients gives

0. 2^{2} + 0. 3^{2} = 0.13

The printed rounded coefficients have norm

S = 0. 2^{2} + 0. 3^{2} + 0. 4^{2} + 0.84 3^{2} = 1.000649.

(1)

Thus the expected rounded answer is $P (E < 6 ϵ) ≃ 0.13$ . If the decimal coefficients are treated as literal exact inputs and the state normalized, the exact probability for that input is $0.13/ S ≃ 0.129916$ . This distinction avoids treating rounding error as a physical departure from wavefunction normalization.

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