 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2012/paper-1/10/ii/solution

Here

p = w = 1

and

q = x^{2}

Q [ψ] = \int_{R} (∣ ψ^{'} ∣^{2} + x^{2} ∣ ψ ∣^{2}) d x

. Admissible trials have a square-integrable weak derivative and finite potential energy; they need not have a classical second derivative everywhere.

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