\[|\Psi_{2}\left(x,y\right)|^{2}=\int_{0}^{\infty}\left(\Psi_{1}\left(\frac{4u^{%
3}+2uy+x}{u^{1/3}}\right)+\Psi_{1}\left(\frac{4u^{3}+2uy-x}{u^{1/3}}\right)%
\right)\frac{\,\mathrm{d}u}{u^{1/3}}.\]