\[\left|\Psi^{(\mathrm{E})}\left(x,y,z\right)\right|^{2}=\frac{8\pi^{2}}{3^{2/3}%
}\int_{0}^{\infty}\int_{0}^{2\pi}\Re\left(\operatorname{Ai}\left(\frac{1}{3^{1%
/3}}\left(x+iy+2zu\exp\left(i\theta\right)+3u^{2}\exp\left(-2i\theta\right)%
\right)\right)\*\operatorname{Bi}\left(\frac{1}{3^{1/3}}\left(x-iy+2zu\exp%
\left(-i\theta\right)+3u^{2}\exp\left(2i\theta\right)\right)\right)\right)u\,%
\mathrm{d}u\,\mathrm{d}\theta.\]