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Archived Calculus for delta function based on wave function

  1. Apr 24, 2013 #1
    1. The problem statement, all variables and given/known data

    Two-electron Wavefunction: ψ(r1,r2,r12) = exp(-Ar1-Br2-Cr12), r12 = |r1-r2|
    A, B, and C are coefficients

    Calculate <ψ|δ(r12)|ψ> and <ψ|δ(r1)|ψ>
    2. Relevant equations

    NO
    3. The attempt at a solution

    <ψ|δ(r12)|ψ>

    = ∫∫dv1dv2ψ2(r1,r2,r12)δ(r12)

    =4π∫dr2ψ2(r2,r2,0)

    <ψ|δ(r1)|ψ>

    = ∫∫dv1dv2ψ2(r1,r2,r12)δ(r1)

    =4π∫dr2ψ2(0,r2,-r2)

    Could you tell me where I am wrong?

    Best regards.
    sandf
     
    Last edited: Apr 24, 2013
  2. jcsd
  3. Jan 3, 2017 #2

    nrqed

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    To be precise, in the last step, one should use that ##r_{12} = |r_1-r_2|= r_2 ## upon setting ##r_1=0##. But other than that, everything is good, one simply has to calculate the integrals which are easy.
     
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