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- https://phys.libretexts.org/Bookshelves/Thermodynamics_and_Statistical_Mechanics/Thermodynamics_and_Statistical_Mechanics_(Nair)/08%3A_Quantum_Statistical_Mechanics/8.05%3A_Applications_of_the_Fermi-Dirac_DistributionWe now consider some applications of the Fermi-Dirac distribution (8.2.5). It is useful to start by examining the behavior of this function as the temperature goes to zero. Thus all states below a cer...We now consider some applications of the Fermi-Dirac distribution (8.2.5). It is useful to start by examining the behavior of this function as the temperature goes to zero. Thus all states below a certain value, which is the zero-temperature value of the chemical potential, are filled with one fermion each. All states above this value are empty. This is a highly quantum state. The value of ϵ for the highest filled state is called the Fermi level.
- https://phys.libretexts.org/Bookshelves/Thermodynamics_and_Statistical_Mechanics/Thermodynamics_and_Statistical_Mechanics_(Nair)/08%3A_Quantum_Statistical_Mechanics/8.01%3A_Prelude_to_Quantum_Statistical_MechanicsThere are two kinds of particles from the point of view of statistics, bosons and fermions. The corresponding statistical distributions are called the Bose-Einstein distribution and the Fermi-Dirac di...There are two kinds of particles from the point of view of statistics, bosons and fermions. The corresponding statistical distributions are called the Bose-Einstein distribution and the Fermi-Dirac distribution. Bosons have the property that one can have any number of particles in a given quantum state, while fermions obey the Pauli exclusion principle which allows a maximum of only one particle per quantum state. Any species of particles can be put into one of these two categories.
- https://phys.libretexts.org/Bookshelves/Thermodynamics_and_Statistical_Mechanics/Thermodynamics_and_Statistical_Mechanics_(Nair)/08%3A_Quantum_Statistical_Mechanics/8.03%3A_Fermi-Dirac_DistributionThe counting of distinct arrangements for fermions is even simpler than for the Bose-Einstein case, since each state can have an occupation number of either zero or 1. Thus consider g states with n pa...The counting of distinct arrangements for fermions is even simpler than for the Bose-Einstein case, since each state can have an occupation number of either zero or 1. Thus consider g states with n particles to be distributed among them. There are n states which are singly occupied and these can be chosen in g!(n!(g−n)!) ways.
- https://phys.libretexts.org/Bookshelves/Thermodynamics_and_Statistical_Mechanics/Essential_Graduate_Physics_-_Statistical_Mechanics_(Likharev)/02%3A_Principles_of_Physical_Statistics/2.08%3A_Systems_of_independent_particlesHowever, it is convenient to keep, for the time being, the discrete-state language, with the understanding that the average number ⟨Nk⟩ of particles in each of these states, usually...However, it is convenient to keep, for the time being, the discrete-state language, with the understanding that the average number ⟨Nk⟩ of particles in each of these states, usually called the state occupancy, is very small.
