DanSandberg
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Linear Polarisability \alpha_{ij} is the amplitude of the electric field induced in the molecule in the i direction given a unit amplitude field in the j direction, hence
E_i^{induced} = \alpha_{ij} E_j^{incident}
(observing summation convention)
Extending this physical interpretation, \beta_{ijk} (X2) is the amplitude of the electric field induced in the i direction given an unit incident field in the j direction applied after unit incident field in the k direction has already been applied, so
E_i^{induced} = \beta_{ijk} E_j^{incident2} E_k^{indicent1}
But there is a third-order term (and fourth-order and fifth-order, etc.) so what do the indices represent in these cases?
Also, there is only one applied (indicent) field so what does it mean to say "the incident field in the j direction" compared to "the incident field in the k direction"?
E_i^{induced} = \alpha_{ij} E_j^{incident}
(observing summation convention)
Extending this physical interpretation, \beta_{ijk} (X2) is the amplitude of the electric field induced in the i direction given an unit incident field in the j direction applied after unit incident field in the k direction has already been applied, so
E_i^{induced} = \beta_{ijk} E_j^{incident2} E_k^{indicent1}
But there is a third-order term (and fourth-order and fifth-order, etc.) so what do the indices represent in these cases?
Also, there is only one applied (indicent) field so what does it mean to say "the incident field in the j direction" compared to "the incident field in the k direction"?