Lecture Notes2

# E k 2 h n 2 n 2 n 2 where a 2 v 23 and n n n

This preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: degree of freedom of the molecular. Q= 2. Examples: a) The translation motion, H = 1 2 2 2 ( px + p y + pz ) 2m (7-8) (7-10) 6 β ( px + p y + pz ) 2 2πmkT 3 / 2 1 V∞ qclass ~ 3 ∫ ⋅ ⋅∫ exp{− }dp x dp y dp z dxdydz = 3 {∫ e − βp / 2 m dp}3 = ( )V h 2m h −∞ h2 pφ 2 1 2 ( pθ + ) b) The rigid rotor, H = 2I sin 2 θ 2π π 1∞ 8πIkT q rot ~ 2 ∫ ∫ dpθ dpφ ∫ dφ ∫ dθe − βH = 0 0 h −∞ h2 p2 k 2 c) The classical harmonic oscillator, H = +x 2µ 2 ∞ 1 k 1/ 2 1∞ 2πkT µ 1/ 2 kT () = , qvib ~ ∫ dp ∫ dxe − βH = ν= () −∞ −∞ h h k νh 2π µ 2 2 2 Chatpter 10 Quantum Statistics − βε k Ξ(V, T, λ ) = ∏ 1 ± λe k − βε k λe N=∑ − βε k k 1 ± λe − βε k λe nk = − βε k 1 ± λe − βε k λε k e E=∑ − βε k k 1 ± λe ±1 , where β = 1 βµ and λ = e kT (I) Weakly Degenerate Fermi - Dirac Gas N=∑ k λe − βε 1 ± λe k − βε k − βε k PV = kT ∑ ln 1 + λe k 2 h n 2 + n 2 + n 2 where a 2 = V 2/3 and n , n , n = 1,2... ε n ,n ,n = x x xyz xyz 2/3 x 8mV 3/ 2 ∞ 1/ 2 − βε 2m λε e dε N = 2π V∫ 2 0 1 + λe − βε h 7 3/ 2 ∞ − βε V ∫ ε 1/ 2ln 1 + λe 0 l +1 N 1 ∞ (− 1) λl =ρ= ∑ V Λ3 l =1 l 3 / 2 2m PV = 2πkT 2 h l +1 1 ∞ (− 1) λl P = ∑ kT Λ3 l =1 l 5 / 2 dε 1/ 2 h2 where Λ = 2πmkT λ = a 0 + a1 ρ + a 2 ρ 2 + ... 2 3 , a − a1 = 0, a −...
View Full Document

## This document was uploaded on 03/26/2014 for the course PH 641 at NJIT.

Ask a homework question - tutors are online