# Vector Integral

1. Oct 14, 2006

### Zelos

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:

• ###### QM Eng.doc
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2. Oct 14, 2006

### HallsofIvy

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

3. Oct 14, 2006

### 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

4. Oct 14, 2006

### 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.

5. Oct 15, 2006

### Zelos

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

6. Oct 15, 2006

### 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?

#### Attached Files:

• ###### QM Eng.doc
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7. Oct 15, 2006

### HallsofIvy

Staff Emeritus
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. Oct 15, 2006

### 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?

9. Oct 15, 2006

### Zelos

i get a infinite integral then wich aint realistic

10. Oct 16, 2006

### 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 $$r_1$$?

11. Oct 17, 2006

### 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

12. Oct 18, 2006

### dextercioby

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

Daniel.

13. Oct 18, 2006

### Zelos

im using spherical