English: A gaussian wave packet. The color (yellow green blue) indicates the phase of the wave function ${\displaystyle \psi }$, its intensity indicates ${\displaystyle |\psi |^{2}/|\psi |_{max}^{2}}$. This wave function could represent the motion of a quantum particle. The wave function is ${\displaystyle \psi (x,y,t)=\psi (x,t)\psi (y,t)}$, ${\displaystyle k_{0x}=k_{0}}$, ${\displaystyle k_{0y}=0}$, ${\displaystyle \psi (x,t)=({\frac {2a^{2}}{\pi }})^{1/4}{\frac {e^{i\phi }}{(a^{4}+{\frac {4\hbar ^{2}t^{2}}{m^{2}}})^{1/4}}}e^{ik_{0}x}exp[-{\frac {(x-{\frac {\hbar k_{0}}{m}}t)^{2}}{a^{2}+{\frac {2i\hbar t}{m}}}}]}$ where ${\displaystyle \phi =-\theta -{\frac {\hbar k_{0}^{2}}{2m}}t}$ and ${\displaystyle tg(2\theta )={\frac {2\hbar t}{ma^{2}}}}$ (source: Cohen-Tannoudji, Diu & Laloë, Quantum Mechanics, complement G_I, §3-a). The Python file which generated this animation is Here.