Homework Statement
The Planck blackbody spectrum is given by
u(ω,t)=\frac{ħω^3}{π^2c^3(e^{βħω}-1)}
Show that the peak of the Planck spectrum for a blackbody at a temperature T occurs at the wavelength
λ_{max}T=0.29
where T is in Kelvin and λmax is in cm.
Homework Equations...
Homework Statement
I'm calculating the coefficients for the Fourier series and I got to part where I can't simplify an any further but I know I have to.
a_n = \frac{1}{2π}\Big[\frac{cos(n-1)π}{n-1}-\frac{cos(n+1)π}{n+1}-\frac{1}{n-1}+\frac{1}{n+1}\Big]Homework EquationsThe Attempt at a...
So I have a long mess of an answer that I won't put up cos it seems pointless. I'm fairly sure it was all differentiated correctly though. For the spherical part do I just start again and change ##z## to ##rcos\theta##?
I know that's the obvious answer but I thought it was to do with what the power was. So I have to differentiate:
##\frac{cz}{(x^2+y^2+z^2)^{\frac{3}{2}}}##
With respect to x,y and z?