[CSC 335] My problem on HW4

[Andrew J. Pounds]

So the r^2 term in the integral is part of the volume element when 
integrating in spherical-polar coordinates.  The r term sandwiched 
between the two wavefunctions is part of the "expectation value" 
operator.   The 4Pi on the outside is due to integrating in spherical 
polar coordinates over an entire sphere.

That said, the argument for your integral in Python would look like...

def fofx(x):
     r = x*0.529e-10
     Z = 1.0
     a0 = 0.529e-10
     a = 1.0 / (4.0 * math.sqrt(2.0*math.pi))*math.pow(Z/a0,3.0/2.0)
     b = 2.0 - Z/a0*r
     c = math.exp(-(Z/a0*r)/2.0)
     psi = a*b*c
     return psi*psi*math.pow(r,3)

Use this for the argument of your quadrature algorithm and then take 
that result and multiply it by 4Pi  to get the expectation value of 
position in units of the Bohr atomic radius.


-- 
Andrew J. Pounds, Ph.D.  (pounds_aj at mercer.edu)
Professor of Chemistry and Computer Science
Mercer University,  Macon, GA 31207   (478) 301-5627
http://faculty.mercer.edu/pounds_aj