= Maxwell-Boltzmann vs Bose-Einstein vs Fermi-Diract statisics
{c}
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 `A` and `B` from 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
Both <Bose-Einstein statistics> and <Fermi-Dirac statistics> tend to the <Maxwell-Boltzmann distribution> in the limit of either:
* high <temperature>
* low concentrations
TODO: show on forumulas. TODO experimental data showing this. Please.....