Generate a picture of a symmetric one-dimensional double-well pontetial

double_well_pontential_picture.py

'''
This code generates a picture of a symmetric 
one-dimensional double-well pontetial.
Mahdi Sadjadi, 2017.
'''

import numpy as np 
import matplotlib.pyplot as plt
from matplotlib.ticker import FuncFormatter, MaxNLocator
for param in ['axes.labelsize','xtick.labelsize','ytick.labelsize']:
    plt.rcParams[param] = 15

f = lambda x: (16/(0.5)**4) *  ((x-1/2)**2 -  (0.5)**2/4)**2

fig,ax = plt.subplots(1,1,figsize=(7,7))
x = np.linspace(0,1,100)
ax.plot(x,f(x),'-k',lw=2)
x = np.linspace(0.,0.55,100)
fprime = lambda x: 0.5 * 128 * (x - 1/4)**2
ax.plot(x,fprime(x),color='darkred',linestyle='--',lw=2)
x = np.linspace(0.45,1,100)
fprime = lambda x: 0.5 * 128 * (x - 3/4)**2
ax.plot(x,fprime(x),color='darkred',linestyle='--',lw=2)
ax.annotate('', xy=(0.25, 8.1), xycoords='data', xytext=(0.75, 8.1), textcoords='data',arrowprops={'lw':2,'arrowstyle': '<->'})
ax.annotate('d', xy=(0.5, 8), xycoords='data',xytext=(0.5, 8), textcoords='offset points',fontsize=20)
ax.annotate('', xy=(0.5, 1), xycoords='data', xytext=(0.5, 0), textcoords='data',arrowprops={'lw':2,'arrowstyle': '<->'})
ax.annotate(r'$V_0$', xy=(0.51, 0.42), xycoords='data',xytext=(0.5, 1), textcoords='offset points',fontsize=20)
ax.vlines(0.25, 0, 10, linestyles='dashed')
ax.vlines(0.75, 0, 10, linestyles='dashed')
ax.yaxis.set_ticks([])
ax.xaxis.set_ticks([])
ax.set_xlim(0,1)
ax.set_ylim(-0.01,10)
ax.set_xlabel('x')
ax.set_ylabel('V(x)')
plt.tight_layout()
plt.savefig('./double_well.pdf',dpi=100)
plt.show(fig)