Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 2 / 36E / a

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- Solution a

Solution

For any normalized trial state

ψ

, the spectral expansion gives

⟨ ψ ∣ H ∣ ψ ⟩ \geq E_{0}

. Minimize this Rayleigh quotient over a trial family to obtain the best upper bound.

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