- #1
bamaguy
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Show by direct calculation that Eqs. (4-134) and (4-137) in the textbook by Duderstadt and Hamilton hold, i.e.:(a) ∫ dΩΩiΩj= 4π/3 δij; i,j = x,y,z;
4π(b) ∫ dΩΩxΩyΩz = 0, if l, m, or n is odd.
4π
The integrals are over 4π.
This is part of the derivation of the diffusion equation from the neutron transport equation. Part (b) from D&H Next note that the integral of the product of any odd number of components of OMEGA vanishes by symmetry.
(a) I think that 4π/3 comes from the volume of the sphere and δij is the kronecker delta. I don't know how to show this mathematically.
(b) I think that this has to do with the sin or cos function.
4π(b) ∫ dΩΩxΩyΩz = 0, if l, m, or n is odd.
4π
The integrals are over 4π.
This is part of the derivation of the diffusion equation from the neutron transport equation. Part (b) from D&H Next note that the integral of the product of any odd number of components of OMEGA vanishes by symmetry.
(a) I think that 4π/3 comes from the volume of the sphere and δij is the kronecker delta. I don't know how to show this mathematically.
(b) I think that this has to do with the sin or cos function.