Scattering amplitude in scattering from a delta function

[joaosantossilva]

Homework Statement

Show that for a potential of type 𝑉 (𝑟⃗) = 𝑔𝛿 (𝑟⃗), where 𝑔 is a constant and 𝛿 (𝑟⃗) is the delta function of Dirac 3D. Using the Born approximation, determine the scattering amplitude and derive an expression for 𝑔 so that the scattering length is b.

Relevant Equations

f(θ) = C ∫ dr rV(r)sin(qr)

I tried to calculate the Fourier transform to get the amplitude, but I got lost

 

[berkeman]

Welcome to the PF.

Homework Statement:: Show that for a potential of type 𝑉 (𝑟⃗) = 𝑔𝛿 (𝑟⃗), where 𝑔 is a constant and 𝛿 (𝑟⃗) is the delta function of Dirac 3D. Using the Born approximation, determine the scattering amplitude and derive an expression for 𝑔 so that the scattering length is b.
Homework Equations:: f(θ) = C ∫ dr rV(r)sin(qr)

I tried to calculate the Fourier transform to get the amplitude, but I got lost

Fun problem. But per the PF rules, we can only help you after you show your work. Please show what you have done so far. Thanks.