Mademoiselle Fourier :D :D :D :D

for each Fourier wavevector $\bfk$, as \begin{eqnarray} \Psi_a^{L,\bfk}(\bfx) &=& (1/k)\nabla_a \Psi^{\bfk}(\bfx)= i\hat k_a e^{i\bfk\cdot\bfx}, \nonumber\\ \Psi_a^{1,\bfk}(\bfx) &=& \frac{1}{|\bfk\times \hatz|} \left(\nabla \times \hatz \Psi^{\bfk}(\bfx) \right)_a = \frac{1}{|\bfk\times ...