1. import numpy as np

import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D

1. Constants

a = 1.0 hbar = 1.0 m = 1.0 p0 = 0

xmax = 10 ymax = 0.8 zmax = ymax

x = np.linspace(-xmax,xmax, 400)

def psi(x, t):

   r = x
   denominator = a + 1j * hbar * t / m
   psi_val = (a / denominator)**(3/2) * np.exp(-r**2 / (2 * denominator)) * np.exp(1j * r * p0)
   return psi_val

tmax = 10 frames_per_t = 12 t_values = np.linspace(-tmax, tmax, frames_per_t * (tmax * 2))

import os movie_name = "gaussian_wavepacket" dir_path = f"./{movie_name}" for N, t in enumerate(t_values):

   fig = plt.figure(figsize=(20, 20))
   ax = fig.add_subplot(111, projection='3d')
   # ax.set_axis_off()

   Z = psi(x, t)
   ax.plot(x, Z.real, Z.imag, label=f't = {t}', linewidth=4)
   
   ax.set_xlim(-xmax, xmax)
   ax.set_ylim(-ymax, ymax)
   ax.set_zlim(-zmax, zmax)
   
   if not os.path.exists(dir_path):
       os.makedirs(dir_path)

   plt.savefig(f"{dir_path}/{N:03d}.png",bbox_inches='tight')

   plt.close()

import imageio.v3 as iio from natsort import natsorted import moviepy.editor as mp

for dir_path in [dir_path]:

   file_names = natsorted((fn for fn in os.listdir(dir_path) if fn.endswith('.png')))

   # Create a list of image files and set the frame rate
   images = []
   fps = 24

   # Iterate over the file names and append the images to the list
   for file_name in file_names:
       file_path = os.path.join(dir_path, file_name)
       images.append(iio.imread(file_path))

   filename = dir_path[2:]
   clip = mp.ImageSequenceClip(images, fps=fps)
   clip.write_videofile(f"output.mp4")

1. !ffmpeg -y -i output.mp4 -c:v libvpx-vp9 -b:v 0 -crf 10 -c:a libvorbis output.webm