 Solution

ID: past-exam-of-the-chemistry-a-course-of-the-university-of-cambridge/2024/paper-1/a1/a/i/solution

Inside the infinite square well, the stationary wavefunctions can be chosen real:

Ψ_{n} (x) = C_{n} sin \frac{nπ x}{a}, n = 1, 2, 3, \dots, 0 < x < a .

They vanish outside the well and at its impenetrable endpoints. A sine meets the left boundary condition; the right one requires

sin (nπ) = 0

. The putative

n = 0

function is identically zero, so it is not a quantum state. The constants

C_{n}

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