Integral of relative distance–dependent potential

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Homework Help Overview

The discussion revolves around the integral of a potential that depends on relative distances in a physics context, likely involving concepts from calculus and physics related to potential energy or fields.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore different ways to set up the integral, with suggestions to fix one variable and analyze the behavior of the distance between two points. There is also a discussion about the implications of assuming one variable as constant and how that affects the integration process.

Discussion Status

There is a back-and-forth regarding the setup of the problem, with some participants providing insights into the mathematical expressions involved. A clarification about the distance formula is made, which seems to have contributed positively to the understanding of the problem, although no consensus on the overall approach has been reached.

Contextual Notes

Participants are grappling with the assumptions around the variables involved in the integral and the implications of those assumptions on the integration process. The discussion reflects a mix of mathematical exploration and conceptual clarification without definitive conclusions.

Isotropicaf
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Homework Statement
Hello,
Imagine the Hamiltonian of a two-atom molecule, you have the kinetic energy of one+the other and then you have a relative distance potential ( V(|r2-r1|^2), ri is 3 dimensional).
How to change the variable to solve the following integral with infinite limits?
Relevant Equations
Intg( exp( |r2-r1|^2) dr1dr2)
I think its going to be intg(dr2)intg(exp(r^2) dr) or something like that.
 
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Try putting one variable on the axis
 
Abhishek11235 said:
Try putting one variable on the axis
Im sorry, i don't know what you mean by that, you mean i should assume r1 as a constant and analyse how |r2-r1|^2 behaves in this condition ?
 
Isotropicaf said:
you mean i should assume r1 as a constant and analyse how |r2-r1|^2 behaves in this condition ?
No!

##|r_2-r_1|=\sqrt{r_2^2+r_1^2-2r_2 r_1cos\theta}##

Now the integrations are easy!
 
Abhishek11235 said:
No!

##|r_2-r_1|=\sqrt{r_2^2+r_1^2-2r_2 r_1cos\theta}##

Now the integrations are easy!
Oh thanks that totally solved my problem, seems obvious now ahah just to check, the integral of the sum is the sum of the integrals?
 

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