import numpy as np
import pylab as pl

x_max = 10.0
x_vals = np.linspace(-x_max, x_max, 1000)
dx = x_vals[1] - x_vals[0]
gaussian = np.exp(-x_vals * x_vals / 2)

psi_funcs = [gaussian,
             x_vals * gaussian,
             (1 - 2 * x_vals * x_vals) * gaussian,
             x_vals * (1 - (2.0 / 3.0) * x_vals * x_vals) * gaussian]

for psi in psi_funcs:
    a = 1.0 / (np.sqrt(psi.dot(psi)) * dx)
    psi *= a

for psi in psi_funcs:
    pl.plot(x_vals, psi)
    pl.show()