Notes on Blackbody radiation

 Hi folks sorry  I have been silent for a while anyway I have beeen busy for about a year writing up some notes on Blackbody radiation. This is a fairly straightforward run through of the basic ideas of Statistical Mechanics and how Planck managed to finally obtain the correct formula by making the guess that electromagneitic energy is quantised. For Planck this was just a ruse and he thought little about it. However it took Einstein to take the idea seriously and he applied it to calculate the specific heat of solids and almost got the correct low temperature behaviour. It was left to Debye to improve on Einstein's model by performing a numerical integration over all frquencies. So Debye is a better physicist than Einstein 😅😅Well at least in that respect. 

I must admit I have had a love hate relationship with Statistical Physics over the years we had a pretty bad lecturer a certain Dr Jones at Exeter university who was (is) a really clever guy but his lectures bore no real resemblance to conventional statistical physics texts and so I and a friend who I was studying with at the time were left scratching our heads and wondering what the subject was all about. With these set of notes I have finally laid the ghost of that experience to reat and now feel I have enough background in statistical physics to understand its applications in Astro-physics especially the physics of the early universe and the calculation of the Helium abundance in the universe by Peebles and other people. 

Of course everyone knows that the Cosmic Background radiaton is a black body and I produce a graph comparing Planck's formula with the FIRAS data obtained from the COBE satellite. I also show how to do the Numerical Integration to get Debye's prediction of the specific heat of silver at low temperatures. 

There are some pretty interesting integrals which invove the Product of the Riemann Zeta function and the Gamma Function. and I show how these are derived unlike most books which just state the formula. As this formula is ubiquitous in Astro-Physical applications then I have enclosed it in a red box at the end of a fairly long appendix at the end. 

Anyway I hope you find the notes useful I now have all the building blocks in place to understand the Peebles calculation and over the next year or two I hope to finally finish this culminating in a code which traces the abundance of the Light elements during the first three minutes after the biig bang 

Here is a link to the file 

https://drive.google.com/file/d/11tpWAP4vh1ywl9ITv8opKCCsiJBws2oP/view?usp=sharing