\[|\Psi_{3}\left(x,y,z\right)|^{2}=2^{4/5}\int_{-\infty}^{\infty}\Psi_{3}\left(2%
^{4/5}(x+2uy+3u^{2}z+5u^{4}),0,2^{2/5}(z+10u^{2})\right)\,\mathrm{d}u.\]