deletions | additions       diff --git a/untitled.tex b/untitled.tex  index c9ba12a..b786719 100644  --- a/untitled.tex  +++ b/untitled.tex 
...
for any value of $n$! That is the entropy of each state is the same, independant of the level of excitation.  When adjusting for waves of any amplitude $\alpha$ we get \begin{equation}  \int_0^\pi \alpha^2sin^2(nx)\mathrm{ln} \alpha^2sin^2(nx) \; dx =\frac{\pi\alpha^2}{2}(1-\mathrm{ln}(4\alpha^2)) =\frac{-\pi\alpha^2}{2}(1-\mathrm{ln}(\frac{4}{\alpha^2}))  \end{equation}