A good conceptual starting point is to like the example that is mentioned at The Harvest of a Century by Siegmund Brandt (2008).
Consider a system with 2 particles and 3 states. Remember that:
- in quantum statistics (Bose-Einstein statistics and Fermi-Dirac statistics), particles are indistinguishable, therefore, we might was well call both of them
A, as opposed to
Bfrom non-quantum statistics
- in Bose-Einstein statistics, two particles may occupy the same state. In Fermi-Dirac statistics
Therefore, all the possible way to put those two particles in three states are for:
- Maxwell-Boltzmann distribution: both A and B can go anywhere:
State 1 State 2 State 3 AB AB AB A B B A A B B A A B B A
- Bose-Einstein statistics: because A and B are indistinguishable, there is now only 1 possibility for the states where A and B would be in different states.
State 1 State 2 State 3 AA AA AA A A A A A A
- Fermi-Dirac statistics: now states with two particles in the same state are not possible anymore:
State 1 State 2 State 3 A A A A A A
Most applications of the Maxwell-Boltzmann distribution confirm the theory, but don't give a very direct proof of its curve.
Here we will try to gather some that do.
Measured particle speeds with a rotation barrel! OMG, pre electromagnetism equipment?
Is it the same as Zartman Ko experiment? TODO find the relevant papers.