 Solution

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

The quantum variational principle says that every admissible nonzero trial wavefunction obeys

E = \frac{⟨ Ψ ∣ H ^ ∣ Ψ ⟩}{⟨ Ψ ∣ Ψ ⟩} \geq E_{0},

where

E_{0}

is the ground-state energy. Thus the Rayleigh quotient is an upper bound. Equality holds when the trial lies entirely in the ground-state subspace.

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