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E radial equation for a hydrogenic atom

  1. Oct 19, 2016 #1
    1. The problem statement, all variables and given/known data
    By substituting R(r)=r^2*e^(-r/a) into the radial equation for a hydrogenic atom, find the values of a, ℓ and E for which the function R(r).


    2. Relevant equations
    http://puu.sh/rOJQ3/8bcad54c45.png [Broken]

    3. The attempt at a solution
    I took the first derivative of R(r), then multiplied it by r^2 before taking the derivative again to get

    e^(-r/a)*(r^4/a - 6r^3/a + 6r^2)
    then when putting it back into the radial equation ended with

    -h^c/m * e^-r/a (r^2/(2a^2) - 3r/a + 3) + (h^2l(l+1))/2m) e^-r/a - (ze^2)/(4pi*epsilon_0)*r*e^(-r/a) = E*R(r)

    then dividing by R(r) = r^2*e^(-r/a) i got

    -h^2*c/(mr^2) (r^2/2a^2 - 3r/a + 3) + h^2l(l+1)/2mr^2 - ze^2/4pi*ep_0 = E

    I dont really know where to go next with this to find E,a, and L.

    thanks
     
    Last edited by a moderator: May 8, 2017
  2. jcsd
  3. Oct 20, 2016 #2
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