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 Hydrogen ground state integral
#1
The integral is supposed to return one but it returns zero.
https://quantummechanics.ucsd.edu/ph130a...de233.html
The integral I'm doing is shown in the link above in the section that says "The radial wavefunctions should be normalised as below." I'm using R_10 which is the ground state.

import scipy
from scipy import constants
import math
import numpy as np
from numpy.polynomial import Laguerre
from scipy import special
import sympy
from sympy import *
from sympy import var
from sympy import integrals
from scipy import integrate

#constants
a_0 = scipy.constants.value('Bohr radius')
e = scipy.constants.value('elementary charge')
hbar = scipy.constants.value('Planck constant over 2 pi')
a = a_0


def int3(x):
    c1 = (2/a)**(1.5)
    y1 = c1*np.exp(-x/a)
    m = np.conjugate(y1)*y1*x**2
    return m
     
I3= integrate.quad(int3, 0, np.inf)
print(I3) 
Thank you in advance
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#2
is it really zero, or .99999999999999999999999991 ?
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#3
The output should be 1 or close to one like 0.99999999... for all values of 'a' in the code. But as i make a smaller in this equal to the bohr radius a_0 it becomes zero.
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