User:Thierry Dugnolle/Python/Wave-packet



A gaussian wave packet. The color (yellow green blue) indicates the phase of the wave function $$\psi$$, its intensity indicates $$| \psi | ^2 / | \psi |_{max} ^2$$. This wave function could represent the motion of a quantum particle. The wave function is $$\psi(x,y,t)=\psi(x,t) \psi(y,t)$$, $$k_{0x}= k_0$$, $$k_{0y}=0$$, $$ \psi (x,t) = (\frac{2a ^2}{\pi}) ^{1/4} \frac{e ^{i \phi}}{(a ^4 + \frac{4 \hbar ^2 t ^2}{m ^2}) ^{1/4}} e ^{i k_0 x} exp [ - \frac{(x - \frac{\hbar k_0}{m} t ) ^2 }{a ^2 + \frac{2 i \hbar t}{m} } ]$$ where $$ \phi = - \theta - \frac{\hbar k_0 ^2}{2 m} t$$ and $$tg (2 \theta) = \frac{2 \hbar t}{m a ^2}$$ (source: Cohen-Tannoudji, Diu & Laloë, Quantum Mechanics, complement GI, §3-a)