Summary

{{Information |description={{en|1=The Wigner function of a simple harmonic oscillator at different levels of excitations. The ${\displaystyle (q,p)}$ are rescaled by ${\displaystyle {\sqrt {n+1}}}$ in order to show that the Wigner function oscillates within that radius, and decays rapidly outside of that radius.

{{Created with code|l1=matplotlib|c1= import numpy as np from scipy.special import laguerre import matplotlib.pyplot as plt from matplotlib import cm

def Wigner(n, q, p):

 r_squared = (n+1) * (q**2 + p**2)
 return ((-1)**n / (np.pi)) * np.exp(-2 * r_squared) * laguerre(n, monic=False)(4 * r_squared)

q = np.linspace(-1, 1, 100) p = np.linspace(-1, 1, 100) Q, P = np.meshgrid(q, p)

n_values = [[0, 1, 2],

           [5, 10, 20]]

plot_y = len(n_values[0]) plot_x = len(n_values) image_width = 6 fig, axes = plt.subplots(plot_x, plot_y, figsize=(image_width*plot_y, image_width*plot_x), subplot_kw={"projection": "3d"})

for i in range(plot_x):

 for j in range(plot_y):
   n = n_values[i][j]
   W = Wigner(n, Q, P)
   ax = axes[i][j]
   ax.contourf(Q, P, W, zdir='z', offset=-1/(np.pi), cmap='coolwarm')
   ax.contourf(Q, P, W, zdir='x', offset=-1, cmap='coolwarm', alpha=0.8)
   # ax.contourf(Q, P, W, zdir='y', offset=3, cmap='coolwarm')

   ax.plot_surface(Q, P, W, vmin=W.min() * 2, cmap=cm.Blues, alpha=0.8)
   ax.set_title(f"n = {n}")

   # ax.set_xlabel("q")
   # ax.set_ylabel("p")
   ax.set_zlim(-1/(np.pi), 1/(np.pi))

plt.tight_layout() plt.savefig("wigner_sho.png") plt.show() }} }} |date=2024-08-28 |source=Own work |author=Cosmia Nebula }}

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Category:CC-BY-SA-4.0#Wigner%20function%20of%20simple%20harmonic%20oscillator.pngCategory:Self-published work