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y i1. y i2. y i3. y i2. y i2. y i3. y i4. y i5. y i6. NON Bolztmann ensembles. Fermions: 2 particles cannot occupy the same quantum state occupation number n k can only be 0 or 1. P 1,2 y =- y antisymmetric.
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yi1 yi2 yi3 yi2 yi2 yi3 yi4 yi5 yi6 NON Bolztmann ensembles Fermions: 2 particles cannot occupy the same quantum stateoccupation number nk can only be 0 or 1 P1,2y=-y antisymmetric Bosons: 2 particles can occupy the same quantum stateoccupation number nk can have any value P1,2y=+y symmetric
Partition function for FD and BE Fermi-Dirac Bose-Einstein
Weakly degenerate Fermi Dirac ideal gas For small deviations from classical behavior, we can use expansions on l to obtain corrections to Bolztmann