Question

Write down a python program to plot the first four energy eigenfunctions.​

Answer 1

this is the python program

import matplotlib.pyplot as plt

import numpy as np

#Constants

h = 6.626e-34

m = 9.11e-31

#Values for L and x

x_list = np.linspace(0,1,100)

L = 1

def psi(n,L,x):

   return np.sqrt(2/L)*np.sin(n*np.pi*x/L)

def psi_2(n,L,x):

   return np.square(psi(n,L,x))

plt.figure(figsize=(15,10))

plt.suptitle("Wave Functions", fontsize=18)

for n in range(1,4):

   #Empty lists for energy and psi wave

   psi_2_list = []

   psi_list = []

   for x in x_list:

       psi_2_list.append(psi_2(n,L,x))

       psi_list.append(psi(n,L,x))

   plt.subplot(3,2,2*n-1)

   plt.plot(x_list, psi_list)

   plt.xlabel("L", fontsize=13)

   plt.ylabel("Ψ", fontsize=13)

   plt.xticks(np.arange(0, 1, step=0.5))

   plt.title("n="+str(n), fontsize=16)

   plt.grid()

   plt.subplot(3,2,2*n)

   plt.plot(x_list, psi_2_list)

   plt.xlabel("L", fontsize=13)

   plt.ylabel("Ψ*Ψ", fontsize=13)

   plt.xticks(np.arange(0, 1, step=0.5))

   plt.title("n="+str(n), fontsize=16)

   plt.grid()

plt.tight_layout(rect=[0, 0.03, 1, 0.95])

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