Help Needed: Solving a Complex Math Integral in Spherical Coordinates

[Zelos]

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 which 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

 

[HallsofIvy]

Is that a $\vec{Z}$ in the exponent? What does that mean?

 

[Zelos]

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

 

[StatusX]

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.

 

[Zelos]

yes, but how do i deal with it when it comes to the 1/|R1-R2| part?

 

[Zelos]

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?

 

[HallsofIvy]

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.

 

[Zelos]

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?

 

[Zelos]

i get a infinite integral then which aint realistic

 

[shmoe]

What do you get as an "infinite integral"? They look like they converge to me (assuming that $\vec{Z}$ is positive). What did you get for the inner integrals, the ones over $$r_1$$?

 

[Zelos]

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

 

[dextercioby]

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

Daniel.

 

[Zelos]

im using spherical