ABSTRACT
Using the Planck’s formula for P n , show that
The average number of photons is given by () 〈 n 〉 = 1 e x − 1 , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429092053/5e12ab0e-ba42-4caa-9bdf-6325e9117d3e/content/eqn4_1.tif"/>
where x = ℏ ω k B T https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429092053/5e12ab0e-ba42-4caa-9bdf-6325e9117d3e/content/ineqn4_1.tif"/> , and k B is the Boltzmann constant.
Show that for large temperatures (T ≫ 1), the average energy is proportional to temperature, i.e., 〈E〉 = k B T.
Calculate 〈n 2〉 and show that the ratio () α = 〈 n 2 〉 − 〈 n 〉 〈 n 〉 2 = 2 . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429092053/5e12ab0e-ba42-4caa-9bdf-6325e9117d3e/content/eqn4_2.tif"/>
