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Homework Help: Interesting integral involving modulus of difference of vectors, how to solve?

  1. Aug 27, 2010 #1
    Hi guys,

    1. The problem statement, all variables and given/known data
    how do i solve (or approximate if not solvable) this integral

    [tex]\int\int e^{-\alpha(|\vec{r}_1-\vec{r}_2|-r_0)^2} d^3\vec{r}_1 d^3\vec{r}_2[/tex]

    [tex]\alpha>0[/tex]

    2. Relevant equations
    none

    3. The attempt at a solution
    none
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Aug 27, 2010 #2

    hunt_mat

    User Avatar
    Homework Helper

    Compute:
    [tex]
    |r_{1}-r_{2}|^{2}=(r_{1}-r_{2}).(r_{1}-r_{2})
    [/tex]
    What do you get? Or take an easier example, can you compute:
    [tex]
    \int\int e^{-\alpha (|x-y|-a)^{2}}dxdy
    [/tex]
     
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