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Vector Integral

  1. Oct 14, 2006 #1
    Im new to this forum but not new to science and math at all. But i have a mathematical problems. Ive been working with QM for a while and im having problem with this specefic integral.
    This integral that is included in the word file is the integral im having problems with. In my papers the R1/R2 is written like r1/r2 is but in bold so i suspect its vector wich would make sense and this is in spherical coordinates. So r1/r2 is then i guess the radius component of R1/R2. How do integrate this? i wish to see it step by step and im glad for any help i can get.

    PS i hope this is the right forum

    Attached Files:

  2. jcsd
  3. Oct 14, 2006 #2


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    Is that a [itex]\vec{Z}[/itex] in the exponent? What does that mean?
  4. Oct 14, 2006 #3
    its a constant, in this case the effective nuclear charge the electron feel since the electrons are mutaly screening each other partly from the nucleus
  5. Oct 14, 2006 #4


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    Is that supposed to be a volume integral? If so, you can start by taking R1 as fixed, and integrating over R2 in spherical coordinates, taking theta=0 along R1.
  6. Oct 15, 2006 #5
    yes, but how do i deal with it when it comes to the 1/|R1-R2| part?
  7. Oct 15, 2006 #6
    ive manished to get this (from some searching on the net) how do i deal with integrals in integrals that contain the outer integrals variable in the integral limits?

    Attached Files:

  8. Oct 15, 2006 #7


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    Just evaluate it normally. The "outer integrals variable in the integral limits" will then be part of the function to be integrated in the second integral.
  9. Oct 15, 2006 #8
    so i just take like normal integration? End - begining? in this case take the integration infinite - integration 0 and put this 2 values as integration limits in the inner integral as it says in the formula?
  10. Oct 15, 2006 #9
    i get a infinite integral then wich aint realistic
  11. Oct 16, 2006 #10


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    What do you get as an "infinite integral"? They look like they converge to me (assuming that [itex]\vec{Z}[/itex] is positive). What did you get for the inner integrals, the ones over [tex]r_1[/tex]?
  12. Oct 17, 2006 #11
    if we concentrate on the 2 integrals that is inside another one its the right one with r1 that i get to be infinite since it goes to infinite and is just r1 since the e^stuff is changed by r2. but i suspect there might be a print error
  13. Oct 18, 2006 #12


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    What coordinate system are you using ? Since it looks as a bicentrical problem, i advise you to use elliptic coordinates.

  14. Oct 18, 2006 #13
    im using spherical
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