 Solution

ID: past-exam-of-the-chemistry-a-course-of-the-university-of-cambridge/2021/paper-1/a2/b/i/solution

\hat{H} = - \frac{ℏ ^{2}}{2 m} \frac{d ^{2}}{d x ^{2}}, 0 < x < a .

The infinite potential outside imposes the Dirichlet boundary conditions

ψ (0) = ψ (a) = 0

and a zero wavefunction outside the interval. These boundary conditions are part of the Hamiltonian operator, rather than an optional addition.

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