How to Solve Black Body Radiation Problems with Mathematica?

ceyhanb
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Homework Statement



Find the ratio of Rayleigh-Jeans and Planck densities of radiation at the maximum for a black body at T = 5000 K.

Find the frequency of the radiation maximum of a black body at T=3000 K. What part of the electromagnetic radion spectrum does this frequency belong to?

Show that Planck's equation transforms to Rayleigh-Jeans equation at high temperatures (use Series[] function of Mathematica).

Calculate constant b of the second Wien's law (use FindRoot[] of Mathematica)

Derive the relation between the amplitudes in the representation of a plane wave in terms of Cos and Sin waves and in terms of the forward and backward complex exponents




Homework Equations


These questions must be answered with Mathematica...however if someone can give some insight on how to do it by hand, that would be great!


The Attempt at a Solution

 
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Hmmm... so many questions, so little attempt at a solution...

Start with your first question...what are the relevant equations? How does one find the maximum of a function?
 
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This figure is from "Introduction to Quantum Mechanics" by Griffiths (3rd edition). It is available to download. It is from page 142. I am hoping the usual people on this site will give me a hand understanding what is going on in the figure. After the equation (4.50) it says "It is customary to introduce the principal quantum number, ##n##, which simply orders the allowed energies, starting with 1 for the ground state. (see the figure)" I still don't understand the figure :( Here is...
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