Lecture Notes2

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

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

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