Perturb

Perturb - Perturbation Method-Helium 1 2e2 2e2 e2 V(r = 4 r...

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Perturbation Method-Helium r r r 1 2 12 ++ - - V(r) = 1 4 πε o 2e 2 r 1 2e 2 r 2 + e 2 r 12 h 2 2m () 2 1 + 2 2 Ψ + 1 4 o 2e 2 r 1 2e 2 r 2 + e 2 r 12 Ψ=ΕΨ r r 1 2 ++ - - λ e 2 4 o r 12 ––––––––––––––––> λ=0-1 r r r 1 2 12 ++ - - E o E + E o (1) Energy E o E ( o) + E (1) Get first order correction to the energy: H = H o + λ H ' where H o Ψ (o) i = E (o) i Ψ (o) i E i 2245 E (o) i + λ E (1) i expand energy in a power series in λ ; keep only first term E (1) i = < H ' > = Ψ (o) i * H ' Ψ (o) i d τ expectation value of perturbation He atom: E (o) = E 1 + E 2 = -13.6eV(Z 2 /n 2 + Z 2 /n 2 ) E i 2245 E 1 + E 2 + <> e 2
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