python - I can not get an animation in jupyter notebook - Stack Overflow

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When I run the code below in VSC or directly run a script via the command line in linux, I get the sought animation. Since I have done most part of the work in jupyter notebook, which I am running locally (not google colab), I want to get the animation in the jupyter notebook which unfortunately is not providing the animation. I see a plot which is remaining static. Can you help make the animation run in jupyter notebook ? I thank you. Here is the code:

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)

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