At non-relativistic limit, m>>p so let p=0
At non-relativistic limit m>>w,
So factorise out m^2 from the square root to get:
m*sqrt(1+2w(n+1/2)/m)
Taylor expansion identity for sqrt(1+x) for small x gives:
E=m+w(n+1/2) but it should equal E=p^2/2m +w(n+1/2), so how does m transform into p^2/2m?
I am not sure where to start for this. Considering it needs to be demonstrate Balmer Break, I am assuming it needs to be wavelength based. As a result I am assuming I cannot use mean (Kramers) Opacity but rather express in terms of Opacity k= n*sigma/rho.
My thoughts are to use Boltzmann...