Recent content by 014137

Hi there. Interestingly, the introduction of the obliquity factor is an ad-hoc fix by Fresnel. In 1886 Kirchoff gave a full mathematical description which accounts for the behaviour that we see. The obliquity factor falls out of this theory as a limiting case. Within Kirchoff's theory...

Does work for n = 10, look: State 3 x 10, 0, 0 3 x 8, 1, 1 3 x 6, 2, 2 3 x 4, 3, 3 3 x 2, 4, 4 3 x 0, 5, 5 6 x 9, 1...

sorry - i was being silly Sum(n - n1 +1) = Sum(n + 1) - Sum(n1) =(n + 1)*(n + 1) - (1/2)n(n + 1) =(1/2)(n+1)(n+2)

Really? Which ones? The formula can be derived like this: n = n1 + n2 + n3 where 1,2,3 are three orthogonal directions. Choose n1 then n2 + n3 = n - n1 Can always pick n - n1 + 1 different pairs of n2, n3. Sum over n1 from 0 to n: Sum(n - n1 +1) = Sum(n - 1) - Sum(n1) =(n - 1)*(n - 1) -...

Watch out! No that's not right. You can't work it out for the first couple of cases and then presume the trend continues like that. In fact, the degeneracy g(n) is: g(n) = (1/2)(n+1)(n+2)