Is the polarization density term in the electromagnetic wave equation the density of static electric dipole moments or transition dipole moments?
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1 Answer
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Polarization at some point is the average of instantaneous dipole moments of molecules we associate with that point (say, all molecules whose any part is in a ball with radius 10$~\mu\text{m}$), times density of molecules at that point.
If the dipole moments do not change in time, you can call them static, but this is a special case. In general, electric dipole moments change in time, and so can polarization.
Transition dipole moment is something different - it is the off-diagonal element of electric dipole matrix associated with two eigen-functions of Hamiltonian in quantum theory.
answered Jun 25, 2021 at 13:00
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$\begingroup$ Thank you for the answer. Is it correct if I say that transition dipole moment is the change in dipole moment after an electron makes a transition? In that case, does the polarization density depend only on the instantaneous dipole moments and not on the transitions involved? $\endgroup$ Commented Jun 28, 2021 at 10:51
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$\begingroup$ No, transition dipole moment is a technical term referring to a specific matrix element. This element is usually time-independent. Real dipole moment, if it is defined, can vary in time. $\endgroup$ Commented Jun 28, 2021 at 10:59