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VariatTh - Variation Method Helium If you guess a solution...

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Variation Method- Helium If you guess a solution to the Schrödinger Equation, how do you find out how good a guess you have made? H Ψ = E Ψ can't be solved exactly: but you have : Ψ (1) guess Ψ (2) better guess Ψ (3) better yet E E E E exact 1 2 3 The Variation Theorem guarantees that the trial energy is always greater than the exact energy. H Ψ i = E i Ψ i Ψ i * H Ψ i d τ = Ψ i * E i Ψ i d τ solve for E i : E i = Ψ i * H Ψ i d τ Ψ i * Ψ i d τ is exact E i (1) = Ψ i (1)* H Ψ i (1) d τ Ψ i (1)* Ψ i (1) d τ E (1) E by the variation theorem
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