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 # Q 2B


import numpy as np

from math import factorial

from scipy.special import hermite as H

from scipy.integrate import quad

import matplotlib.pyplot as plt


x =np.linspace(-5,5, 1001)


def psi(n):

    return 1/np.sqrt(2**n * factorial(n)) * (1/np.pi)**(1/4) * np.exp(-x**2/2) * H(n)(x)


fig, ax = plt.subplots(1,3, sharex=True)


ax[0].plot(x, psi(2),'r')

ax[0].set_title("$\psi_2$")

ax[0].axhline()

ax[1].plot(x, psi(1),'b')

ax[1].set_title("$\psi_1$")

ax[1].axhline()

ax[2].plot(x, psi(0),'orange')

ax[2].set_title("$\psi_0$")

ax[2].axhline()

plt.show()

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