I am wondering about the partition function of the classical microcanonical ensemble. It contains Planck's constant and also an indistinguishability argument about the particles I am looking at and I find this confusing for the following reasons:
If I describe for example an ideal gas using classical mechanics, there is no reason why I should assume that there is a problem to distinguish the gas molecules or why $\hbar$ should occur there.
I mean, how could people like Gibbs etc. derive this equation if they did not know about QM?
In some sense, there has to be a reason why we have these two QM properties in there and maybe it is just to get the limit to QM right, but is this really the only reason for this?
I would love to receive a few ideas about this strange definition by this community, in order to get impressions, why we model a (NVE) ensemble this way?