def test_Ehrenfest2(sys):
"""
Test the second Ehenfest theorem for the specified quantum system
"""
times = sys.dt * np.arange(len(sys.P_average))
dP_dt = np.gradient(sys.P_average, sys.dt)
print("%.2e" % np.linalg.norm(dP_dt - sys.P_average_RHS))
plt.plot(times, dP_dt, '-r', label='$d\\langle\\hat{p}\\rangle / dt$')
plt.plot(times,
sys.P_average_RHS,
'--b',
label='$\\langle -U\'(\\hat{x})\\rangle$')
plt.legend()
plt.ylabel('force')
plt.xlabel('time $t$ (a.u.)')
def test_Ehrenfest1(sys):
"""
Test the first Ehenfest theorem for the specified quantum system
"""
times = sys.dt * np.arange(len(sys.x_average))
dx_dt = np.gradient(sys.x_average, sys.dt)
print("{:.2e}".format(np.linalg.norm(dx_dt - sys.x_average_rhs)))
plt.plot(times, dx_dt, '-r', label='$d\\langle\\hat{x}\\rangle / dt$')
plt.plot(times,
sys.x_average_rhs,
'--b',
label='$\\langle\\hat{p}\\rangle$')
plt.legend()
plt.ylabel('momentum')
plt.xlabel('time $t$ (a.u.)')