\[|\Psi_{3}\left(x,y,z\right)|^{2}=\frac{2^{7/4}}{5^{1/4}}\int_{0}^{\infty}\Re%
\left({\mathrm{e}}^{2iu(u^{4}+zu^{2}+x)}\Psi_{2}\left(\frac{2^{7/4}}{5^{1/4}}%
yu^{3/4},\sqrt{\frac{2u}{5}}(3z+10u^{2})\right)\right)\frac{\,\mathrm{d}u}{u^{%
1/4}}.\]