There is a detail from a very well-written answer here that interested me. Unfortunately Springer is charging 41 Euros to access the paper cited by the author.
I wonder if someone could elaborate on an assertion about the commutator ($PX - XP = -i \hbar $):
"Heisenberg [cite omitted], realizes that this is a splitting up of phase space into cells of dimension $h$ and uses this to deduce an approximate uncertainty principle."