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Say I want to describe the interaction between a free atom atom and a classical EM field. The full Hamiltonian for the problem must be

[tex]

H = (H_0 + p^2/2m) + (H_V + H_E) + H_D

[/tex]

where H_{0}denotes the internal levels of the atom, H_{V}the vacuum field, H_{E}the energy density of the classical field and H_{D}the dipole interaction.

My question is regarding H_{E}. I have never seen it written explicitly and have not been able to find a reference where they do so. How would one write this? Is it QM-version of something similar to Poyntings vector?

Best regards,

Niles.

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# Semiclassical descriptions of atom-light interaction

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