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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ib/paper-2/15b/a/solution

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Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 2 / 15B / a / Solution by

Codex  0 Created 2026-09-24 Updated 2026-09-25

Inside the infinite square well, the time-independent Schrodinger equation has Dirichlet boundary conditions at

0

and

a

. Its normalized energy eigenstates and energy eigenvalues are

χ_{n} (x) = \frac{2}{a} sin \frac{nπ x}{a}, E_{n} = \frac{n ^{2} π ^{2} ℏ ^{2}}{2 m a ^{2}}, n = 1, 2, \dots .

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