Я не могу получить анимацию в блокноте Jupyter ⇐ Python

[Anonymous]

Когда я запускаю приведенный ниже код в VSC или напрямую запускаю скрипт через командную строку в Linux, я получаю искомую анимацию. Поскольку большую часть работы я выполнил в блокноте Jupyter, который запускаю локально (а не в Google Colab), я хочу получить анимацию в блокноте Jupyter, который, к сожалению, не предоставляет анимацию. Я вижу сюжет, который остается статичным. Можете ли вы помочь запустить анимацию в блокноте Jupyter? Я благодарю вас. Вот код:
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation
from numpy.fft import fft, ifft

# Define the kinetic operator (Fourier space)
def kinetic_operator(psi, N, mu, epsilon, tau):
k_vals = np.fft.fftfreq(N, epsilon) * 2 * np.pi # Discrete k-values for FFT
K_vals = (2 * (np.sin(np.pi * k_vals / N)**2) / (mu * epsilon**2)) # Eigenvalues of K
psi_k = fft(psi) # Transform to Fourier space
psi_k = psi_k * np.exp(-1j * tau * K_vals) # Apply kinetic operator in k-space
return ifft(psi_k) # Transform back to real space

# Define the potential operator (diagonal in real space)
def potential_operator(psi, V, tau, half=False):
factor = np.exp(-1j * V * tau / 2) if half else np.exp(-1j * V * tau)
return factor * psi

# Strang splitting integrator
def strang_splitting_integrator(psi, V, N, tau, mu, epsilon):
# Apply half-step potential, full-step kinetic, and another half-step potential
psi_half_potential = potential_operator(psi, V, tau, half=True)
psi_kinetic = kinetic_operator(psi_half_potential, N, mu, epsilon, tau)
psi_new = potential_operator(psi_kinetic, V, tau, half=True)
return psi_new

# Animation function with optimizations
def animate_wavefunction(N, V, psi0, mu, epsilon, tau, steps=200, interval=50):
x = np.linspace(0, N * epsilon, N)
psi = np.copy(psi0) # Starting point for the wavefunction

fig, ax = plt.subplots()
line_prob, = ax.plot(x, np.abs(psi)**2, color='g', linestyle='--', label="Probability density")
ax.set_ylim(0, 1) # Adjust based on the scale of |psi|^2
ax.set_xlim(0, N * epsilon)
ax.set_title("Time Evolution of Wavefunction")
ax.set_xlabel("Position")
ax.set_ylabel("Probability Density")
#plt.show()

# The update function for the animation
def update(frame):
nonlocal psi # Ensure we update the original psi
# Update the wavefunction using Strang-Splitting integrator
psi = strang_splitting_integrator(psi, V, N, tau, mu, epsilon)
line_prob.set_ydata(np.abs(psi)**2) # Update probability density
return line_prob, # Return the updated line object for blitting

# Create the animation using FuncAnimation
ani = FuncAnimation(fig, update, frames=range(steps), interval=interval)#, blit=True)
plt.show()
return ani

# Set up parameters for the simulation
N = 200 # Decrease the number of lattice points to improve performance
mu = 1.0 # Mass of particle
epsilon = 0.1 # Small spatial grid spacing for a better approximation of the continuum
tau = 0.1 # Time step for accurate evolution
steps = 200 # Number of time steps for animation

# Initial wavefunction (Gaussian wave packet)
x = np.linspace(0, N * epsilon, N)
psi0 = np.exp(-(x - N * epsilon / 2)**2 / (2.0 * (N * epsilon / 20)**2))

psi0 /= np.sqrt(epsilon) * np.linalg.norm(psi0) # Normalize wavefunction

# Define potential V (free particle case)
V = np.zeros(N) # No potential energy (free particle)

# Run the animation
ani = animate_wavefunction(N, V, psi0, mu, epsilon, tau, steps=steps, interval=50)


Подробнее здесь: https://stackoverflow.com/questions/792 ... r-notebook