Lecture 17 - 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

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 +...
View Full Document

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.

Page1 / 10

Lecture 17 - 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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online