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Scattering amplitude in scattering from a delta function

Homework Statement:

Show that for a potential of type 𝑉 (π‘Ÿβƒ—) = 𝑔𝛿 (π‘Ÿβƒ—), where 𝑔 is a constant and 𝛿 (π‘Ÿβƒ—) 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
 

Answers and Replies

berkeman
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Welcome to the PF. :smile:
Homework Statement:: Show that for a potential of type 𝑉 (π‘Ÿβƒ—) = 𝑔𝛿 (π‘Ÿβƒ—), where 𝑔 is a constant and 𝛿 (π‘Ÿβƒ—) 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.
 
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