2.4: Higher Orders
- Page ID
- 28742
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It may turn out that the matrix element \(V_{00}\) is zero, often due to symmetry. In this case we must consider what happens at second order. Going back to equation 1, and using our expression for mixing and assumption \(c_{00} \approx 1\)
\[\Delta E_0 = 0 + \sum_{i=1, \infty} \langle n_i | \hat{V} | n_0 \rangle \frac{V_{0i}}{(E_0 − E_i)} = \sum_{i=1, \infty} \frac{|V_{i0}|^2}{(E_0 − E_i)} \nonumber\]