import numpy as np
import matplotlib.pyplot as plt
from scipy import optimize

x=np.arange(0,1,0.0001)
a=float(input("Enter eefective well width ="))
beta=a

def func(x):
  return np.tan(beta*np.sqrt(x))-np.sqrt(x*(1-x))/(x-0.5)

nmax=int(np.trunc(beta/np.pi+0.5))+1
xdata=np.zeros(nmax)

xtest=0
for i in range(nmax):
  xdata[i]=(np.pi*(i+0.5)/beta)**2
  if (i==0):
    continue
  if (xdata[i-1]<0.5 and xdata[i]>0.5):
    xdata[i]=0.5
    xtest=1
    continue
  if (xtest == 1):
    xdata[i]=(np.pi*(i-0.5)/beta)**2
lp=1.0001
rp=0.9999
for i in range(nmax):
 tout=0
 lv=xdata[i]*lp
 if (i == nmax-1):
  rv=1.
 else:
  rv=xdata[i+1]*rp
 if (func(lv)*func(rv)>0):
  tout=1 
 else: 
  root=optimize.brentq(func,lv,rv,xtol=1.e-7,rtol=1.e-8)
 if (tout != 1):
   print ("For energy level",i,"E/Uo is:",root)