Vector Integral

  • Thread starter Zelos
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  • #1
Zelos
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Im new to this forum but not new to science and math at all. But i have a mathematical problems. I've been working with QM for a while and I am having problem with this specefic integral.
This integral that is included in the word file is the integral I am 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 I am glad for any help i can get.

PS i hope this is the right forum
 

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  • #2
HallsofIvy
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Is that a [itex]\vec{Z}[/itex] in the exponent? What does that mean?
 
  • #3
Zelos
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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
 
  • #4
StatusX
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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.
 
  • #5
Zelos
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yes, but how do i deal with it when it comes to the 1/|R1-R2| part?
 
  • #6
Zelos
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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?
 

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  • #7
HallsofIvy
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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.
 
  • #8
Zelos
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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?
 
  • #9
Zelos
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i get a infinite integral then wich aint realistic
 
  • #10
shmoe
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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]?
 
  • #11
Zelos
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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
 
  • #12
dextercioby
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What coordinate system are you using ? Since it looks as a bicentrical problem, i advise you to use elliptic coordinates.

Daniel.
 
  • #13
Zelos
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im using spherical
 

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