 Solution

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

Comparing the variational method estimate with the exact ground-state energy gives

\frac{E}{E _{1}} = \frac{10}{π ^{2}} = 1.01321 \dots > 1.

The estimate is about $1.32%$ too high, consistently with the quantum variational principle. Its closeness does not mean that the trial wavefunction is an exact energy eigenfunction.

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