= Virtual hopping
{title2=$\Delta E^{(2)}=\sum_{a\ne0}|\langle a|T|0\rangle|^2/(E_0-E_a)$}
A hopping process through an intermediate configuration of different unperturbed <energy>, contributing to a low-<energy> effective description through <perturbation theory>. If an intermediate state costs $\Delta>0$, <second-order nondegenerate perturbation theory> gives a contribution $-|\langle a|T|0\rangle|^2/\Delta$. Its amplitude is of order $t/\Delta$ and its <energy> correction of order $-t^2/\Delta$; a degenerate low-<energy> sector requires the corresponding <degenerate perturbation theory> before identifying the <ground state>.
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