= Logarithmic wave perturbation
{title2=$\chi=\log(\psi/\psi_i)$}
The <logarithmic wave perturbation> measures relative <complex amplitude> and phase through $\psi=\psi_i e^\chi$. A continuous branch requires nonzero incident and total fields in the region considered. For the <Helmholtz equation> with <scattering potential> convention $L_0\psi=-V\psi$, its equation is $(\Delta+2\nabla\log\psi_i\cdot\nabla)\chi+\nabla\chi\cdot\nabla\chi=-V$. The dot product is bilinear, not a squared modulus.
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