# Calculus for delta function based on wave function

1. Apr 24, 2013

### sandf

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. Jan 3, 2017

### nrqed

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.