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If I consider a two-level system with a ground and an excited state, I can compute the instantaneous rate at which work is being done on the dipole $\mu(t)$ by an electric field $E(t)$:

$\dot{W} = E(t)\tfrac{\mathrm{d}}{\mathrm{d}t}\mu(t)$

If I integrate over time, I would end up with with the work that is being done on the dipole by the field. What I am interested in is, how can I connect this with the optical absorption due to the dipole transition?

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