Past exam of the chemistry A course of the University of Cambridge / 2021 / Paper 1 / A2 / a / i

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- Solution 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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