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Unformatted text preview: δ ↓ ↑ ? # of available states or T , ⇒ we have to count more carefully N ψ we have to look at the particle's wavefunction ψ i1 ψ i3 ψ i2 Fermions: 2 particles cannot occupy the same quantum state occupation number n k can only be 0 or 1 Bosons: 2 particles can occupy the same quantum state occupation number n k can have any value ψ i4 ψ i6 ψ i5 ψ i2 ψ i3 ψ i2 P 1,2 ψ = ψ antisymmetric P 1,2 ψ =+ ψ symmetric ( 29 μ β μ λ λ Ξ = = ∑ ∑ where we used , , NJ N kT N j E V T e e { } β β ε ∑ = ∑ ∑ a sum over states becomes a sume over each distribution if we consider i NJ i i j E e e n n ( 29 ( 29 βε μ λ = = Ξ = ⋅ ∑ ∏ max V,T, k k k k k e n n n n ( 29 ( 29 βε μ λ = = Ξ = ⋅ ∑ ∏ 1 V, , T k k k k k e n n n ( 29 ( 29 βε μ λ Ξ = + ⋅ ∏ , , 1 k k V T e FermiDirac ( 29 ( 29 βε λ μ =∞ = = ⋅ Ξ ∑ ∏ V, , T k k k k k e n n n ( 29 βε μ λ Ξ = ⋅ ∏ 1 , , 1 k k V T e BoseEinstein ( 29 ( 29 βε μ λ Ξ = ∏ + 1 + , , 1 k k V T e ( 29 βε βε λ λ = ∑ ∑ k k +...
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This note was uploaded on 05/29/2011 for the course CHM 6461 taught by Professor Bowers during the Spring '08 term at University of Florida.
 Spring '08
 Bowers

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