So a quick question. If im representing a quantum gas with diagrams of the allowed configurations of the gas.
When it comes to indistinguishable I have 7 configurations. But if we then compare to a gas made up of distinguishable particles.
Would there be more or less configurations if the particles were distinguishable? and is the probability of finding two or more particles in the same state higher or lower than in the case of bosons. What does this imply about the sociability of bosons?
http://www.spacedaily.com/reports/When_Bosons_become_Fermions.html
When representing a quantum gas with diagrams of the allowed configurations, the number of configurations depends on whether the particles are distinguishable or indistinguishable.
In the case of indistinguishable particles, such as fermions or bosons, the configurations are limited by the Pauli exclusion principle for fermions and by Bose-Einstein statistics for bosons.
If you have 7 configurations for indistinguishable particles, let's consider what happens if the particles were distinguishable. In this case, each particle can occupy a specific state independently of others, and there are no restrictions or limitations like those imposed by quantum statistics.
For distinguishable particles, the number of configurations can be calculated by multiplying the number of available states for each particle. So, if there are, for example, 3 possible states and 2 particles, the total number of configurations would be 3 * 3 = 9.
Therefore, when particles are distinguishable, there would generally be more configurations than when they are indistinguishable.
Regarding the probability of finding two or more particles in the same state, in the case of bosons, this probability is higher compared to indistinguishable fermions. This is because bosons can occupy the same quantum state simultaneously, which is known as Bose-Einstein condensation.
This implies that bosons are more sociable compared to fermions. They have a tendency to congregate and occupy the same quantum state, leading to phenomena like superfluidity in liquid helium or the formation of Bose-Einstein condensates at ultra-low temperatures.
In summary, if the particles in a quantum gas are distinguishable, there would generally be more configurations compared to indistinguishable particles. The probability of finding two or more particles in the same state is higher for bosons compared to fermions, indicating greater sociability for bosons.