Harmonic oscillator in phase space: with both quantum and field theoretic hamiltonian

Harmonic oscillator in phase space

import numpy as np
import matplotlib.pyplot as plt

m=1 # mass of the quantum particle oscillating
H=np.array([0.5, 1, 1.5, 2]) # energy values
w=1

# Set canvas to 10 inches wide and 5 inches high
plt.figure(figsize=(7, 5))

for i in H:
    q = np.linspace(-5,5,1000)  # Generating q values to plot
    p = np.sqrt(2*m*i - (m*w*q)**2) # Harmonic oscillator hamiltonian equation in terms of p as we will generate p values for known H and q
    plt.plot(q,p, label=f"H = {i:.1f}") # Plot with energy levels
    plt.plot(q,-p, color=plt.gca().lines[-1].get_color()) # Plot with energy levels as well as matching colors for -ve and +ve p

plt.title("Harmonic Oscillator Phase Space")
plt.xlabel("q")
plt.ylabel("p")
plt.legend(title="Energy Levels (H)", loc="upper right")
plt.grid()
plt.show()

import numpy as np
import matplotlib.pyplot as plt

H = np.array([0.5, 1, 1.5, 2]) # energy values
m = 1 # mass of the quantum particle oscillating
k = 1

w = np.sqrt(k**2 + m**2)
q = np.linspace(-6, 6, 1000) # Generating q values to plot

# Set canvas to 10 inches wide and 5 inches high
plt.figure(figsize=(7, 5))

for i in H:
    p = np.sqrt(2*i - (w*q)**2) # Harmonic oscillator hamiltonian equation in terms of p as we will generate p values for known H and q
    p[p.imag != 0] = np.nan

    plt.plot(q, p, label=f"H = {i:.1f}") # Plot with energy levels
    plt.plot(q, -p, color=plt.gca().lines[-1].get_color()) # Plot with energy levels as well as matching colors for -ve and +ve p

plt.title("Scalar Field Mode Phase Space")
plt.xlabel(r"$\phi_k$")
plt.ylabel(r"$\pi_k$")
plt.legend(title="Energy Levels (H)", loc="upper right")
plt.grid()
plt.show()