9. Counting states Consider a single quantum particle of mass m in a square two-dimensional box of side L. The energy of the particle is E = z 2r 2mizz(n, + n ) with ny, ny = 1, 2,3,..... We can therefore label microstates using the two integer quantum numbers n,, Ry. Let's ask the following question: how many microstates have an energy smaller than some E? In other words, we need to count the number of pairs (n,, n ) such that (n' +2)