Lecture 17 - δ ↓ ↑ of available states or T ⇒ we...

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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 Fermi-Dirac ( 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 Bose-Einstein ( 29 ( 29 βε μ λ- Ξ = ∏ +- 1 +- , , 1 k k V T e ( 29 βε βε λ λ-- = ∑ ∑ k k +...
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Lecture 17 - δ ↓ ↑ of available states or T ⇒ we...

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