Question

15.4.4

For a point source at the origin, the three-dimensional neutron diffusion equation be 15.4.4 comes -Dv2(r)K2D¢(r) = Q8(r) Apply a three-dimensional Fourier transform. Solve the transformed equation. Trans form the solution back into r-space Hint The following equations are useful 1. Vf(r)eikrdr -kl2f(r)ekr d?r (2)E 1 (2T)E p(r)eikr d2r (2n)E 1 2. Let D(k) -ar 1 4T 3. The Fourier transform of f(r) 1S (2m)2+a2

It's in Mathematical Methods for Physicists 6e, Arfken ch15

Please help.

Thank you so much.

Answer 1

The gueu equntien is DD K D 6) for foruicr toatom a conteut n egualien K. ue will se as Take fastin tranfor looth ndes KF(b)0 F(s) - DF(ot)

FCd()) S TAAgine Ciu t Hhe thact F 2ajin -It/ (2 4F()) Caualion ecaes DIk )Ko() F (S)) F() 2 foroperty delt rcen the using fourior tmapm of b) )