 Solution

ID: past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2019/paper-2/section-a-ii/15/ii/solution

The wave function vanishes in regions I and III. In region II it is sinusoidal and satisfies

ψ (0) = ψ (L) = 0

- \frac{ℏ ^{2}}{2 m} \frac{d ^{2} ψ}{d x ^{2}} = E ψ, 0 < x < L .

A nonzero stationary state therefore has standing-wave nodes at the two walls; it cannot have a nonzero constant ground-state wave function.

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