In [90]:
from mayavi import mlab
import numpy as np
from scipy.special import sph_harm
import time
from numpy import sin
from numpy import cos
from matplotlib import pyplot as plt
%matplotlib inline
In [213]:
x_vals = np.linspace(0,1,200)
t_vals = np.linspace(0,np.pi/2,50)
psi = lambda x,t: np.sqrt(2)*(sin(t)*sin(2*x*np.pi)*np.exp(1j*20*t) + cos(t)*sin(1*x*np.pi)*np.exp(1j*1*t))
#psi = lambda x,t: np.sqrt(2)*(0.5*sin(4*x*np.pi) + 0.5*sin(3*x*np.pi)*np.exp(1j*1*t))
In [214]:
z = []
for t in t_vals:
vals = np.conj(psi(x_vals,t))*psi(x_vals,t)
z.append(vals)
z = np.array(z)
levels = np.linspace(np.min(z),np.max(z),100)
plt.contourf(x_vals,t_vals,z, levels = levels)
Out[214]:
In [203]:
for t in np.linspace(0,np.pi/2,40):
vals = psi(x_vals, t)*np.conj(psi(x_vals, t))
plt.plot(x_vals, vals)
print(np.sum(vals))
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