Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Hartree fock derivation problem

  1. Apr 3, 2016 #1
    Can anyone show the algebra that leads to the rewriting that I have underlined in the attachment. It is a derivation

    It is taken from the start of a derivation of the roothans method of hartree fock from 1972 with the authors Snow and Bills.
  2. jcsd
  3. Apr 3, 2016 #2


    User Avatar
    2017 Award

    Staff: Mentor

    Plugging in the Hamiltonian, you can group its terms into three parts:
    One involving only ##\phi_1##-related terms, one only involving ##\phi_2##-related terms, and one with ##r_{12}##. In the first two, you can take the other field out of the integral, where it then cancels the corresponding expression in the denominator.
    Then use the symmetry (1<->2) to combine both simplified fractions. The third fraction from the original expansion just stays as it is.
  4. Apr 3, 2016 #3


    User Avatar
    Gold Member

    write down your Hamiltonian... some part of it is going to see only the [itex]\phi_1[/itex]'s and some other part will only see the [itex]\phi_2[/itex]'s (that's the reason of the 2* integral)....
    So you can break the integral [itex]\int \int f(x_1,x_2) dx_1 dx_2 = \int \int f(x_1) f(x_2) dx_1 dx_2 = \int f(x_1) dx_1 \int f(x_2) dx_2 [/itex]...that's the first integral in your orange... The second integral in your orange comes from the Hamiltonian's part that mixes [itex]r_{1},r_2 \text{ into } r_{12}[/itex] and so your double integral remains : [itex] \int \int f(x_1,x_2) dx_1 dx_2 [/itex] which you cannot seperate.

    I'm pretty sure this should go to quantum physics XD
  5. Apr 3, 2016 #4
    Thanks I did get it from your explanation!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted