Lecture 10

# Lecture 10 - Examples Photon gas an electromagnetic field in thermal equilibrium with its container ϖ ε = = → ∑ h i i In this case h harmonic

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

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Examples: Photon gas, an electromagnetic field in thermal equilibrium with its container ϖ ε = = → ∑ h i i In this case h harmonic oscillator QM we know that i n i H = h To describe the state of the field, we need to know how many n are in each oscillator Photons are bosons x n=0,1,2,3….. ( 29 ( 29 ν ν β β ε ε ε ∞- + + +- = = ∑ ∑ 1 2 1 1 2 2 , ,..., ... Q N,V,T j j j n n n n n n E e e ( 29 ( 29 ( 29 ( 29 ( 29 β β β β ε ε ε ε ∞ ∞ =---- = = ∑ ∑ ∏ L 1 2 1 1 2 2 , ,..., first we want to show that Q N,V,T j j j j j j n n n n j n n n n e e e e ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 β β β β β β β β β ε ε ε ε ε ε ε ε ε- ⋅- ⋅- ⋅- ⋅- ⋅- ⋅- ⋅- ⋅- ⋅ = + + × + + × + + 1 1 1 2 2 2 3 3 3 1 2 1 2 1 2 Q N,V,T e e e e e e e e e ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 β β β β β β β β β β β β ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε + + + + + + + + +- ⋅ ⋅- ⋅ ⋅- ⋅ ⋅- ⋅ ⋅- ⋅ ⋅- ⋅ ⋅- ⋅ ⋅- ⋅ ⋅- ⋅ ⋅- ⋅- ⋅- ⋅ + + + + + + + + × + + = 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 3 3 3 1 2 1 2 1 2 1 1 1 2 2 1 1 2 e e e e e e e e e e e e ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 β β β β β β β β β ε ε ε β ε ε ε β ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε + + + + + + + + + + +- ⋅ ⋅ ⋅- ⋅ ⋅ ⋅- ⋅ ⋅- ⋅ ⋅- ⋅ ⋅ ⋅ ⋅- ⋅ ⋅ ⋅---- ⋅ + ⋅ + ⋅- ⋅ + ⋅ + ⋅ ⋅ + ⋅ + ⋅ ⋅ + ⋅ + ⋅ + ⋅ ⋅ + + + + + + + = + + + + + 1 2 3 1 2 3 1 2 1 2 3 1 2 1 2 3 3 1 1 1 2 3 1 2 3 1 2 3 1 2 1 1 2 3 1 2 3 1 1 2 2 1 2 2 1 2 ... e e e e e e e e e e e ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 β β β β β β β ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε + + ∞ + + + +-- ⋅ ⋅ ⋅ ⋅ ⋅ ⋅----- ⋅ + ⋅ + ⋅ ⋅ ⋅ + ⋅ + + ⋅ + ⋅ ⋅ + ⋅ + ⋅ ⋅ + + = + + + + ∑ 1 2 1 2 3 1 2 3 1 1 2 2 3 3 1 2 1 2 3 1 2 3 1 3 3 2 , ,..., 1 1 1 2 2 ... j n n n n n n e e e e e e e ( 29 ( 29 ( 29 β β ε ε ∞ = =--- = = ∑- ∑ ∏ ∏ j 1 1 where we used 1 Q N,V,T 1 j j j j j x n j j x n e e The average number of photons in a state j… ( 29 { } ν ν ν ν β β ε ε β-- + +- = = ∑ ∑ ∑ 1 1 2 2 j ......
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 / 18

Lecture 10 - Examples Photon gas an electromagnetic field in thermal equilibrium with its container ϖ ε = = → ∑ h i i In this case h harmonic

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

View Full Document
Ask a homework question - tutors are online