import numpy as np
import matplotlib.pyplot as plt
import matplotlib.animation as animation
plt.close('all')

a=0.01
v=0.1

def psi2(x,t):
    return 1/np.sqrt(1+(a*t)**2)*np.exp(-(x-v*t)**2/((1+(a*t)**2)))


fig, ax = plt.subplots()
plt.title("Evolution de $|\psi(x,t)|^2$ pour un paquet d'ondes gaussien")
plt.xlabel('x')


x = np.linspace(-10,100,10000)
line, = ax.plot(x, psi2(x,0))





def animate(t):
    line.set_ydata(psi2(x,t))  # update the data.
    return line


ani = animation.FuncAnimation(
    fig, animate, interval=20)


plt.show()