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I Hartree fock derivation problem

  1. Apr 3, 2016 #1

    georg gill

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    Can anyone show the algebra that leads to the rewriting that I have underlined in the attachment. It is a derivation

    upload_2016-4-3_15-8-17.png
    upload_2016-4-3_15-8-34.png
    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

    mfb

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    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

    ChrisVer

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    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

    georg gill

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    Thanks I did get it from your explanation!
     
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