import numpy as np import matplotlib.pyplot as plt  def rho_w_star(l, w):   if w > np.sqrt(2):     if -np.sqrt(2) <= l <= np.sqrt(2):       return (1 / np.pi) * np.sqrt(2 - l**2)     else:       return 0   else:     L_w = (2 * np.sqrt(w**2 + 6) - w) / 3     if -L_w <= l <= w:       return (np.sqrt(l + L_w) / (2 * np.pi * np.sqrt(w - l))) * (w + L_w - 2 * l)     else:       return 0  lambda_values = np.linspace(-2, 2, 500) plt.figure(figsize=(12, 6))  for w in [-1.5, -1, 0, 1, 1.3, 1.5]:     plt.plot(lambda_values, [rho_w_star(l, w) for l in lambda_values], color='blue', alpha=0.6)     plt.axvline(x=w, color='black', linestyle='--', alpha=0.6)  # semilogy plt.semilogy() plt.xlabel("$\lambda$") plt.ylabel("$\rho_w^*(\lambda)$") plt.title("Coulomb Gas distribution for various wall positions") plt.savefig('Coulomb Gas distribution for various wall positions.svg') plt.show()