Chapter 13 (II)

# Chapter 13 (II) - 13.2 Fermi-Dirac Statistics j j j j j N g...

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Unformatted text preview: 13.2 Fermi-Dirac Statistics . )! ( ! ! j j j j j N g N g − = ω . )! ( ! ! ) ,... , ( 1 2 1 ∏ = − = = n j j j j j n FD N g N g N N N ω ω We want to get the equilibrium configuration for a system consisting of fermion particles, such as electrons and protons. The number of ways to arrange N j indistinguishable particles into energy level ε j with g j quantum states with no more than one particle in each state (the Pauli exclusive principle) is equal to the number of ways to put distinguishable g j particles into N j occupied and g j-N j unoccupied states: Thus, the number of microstates for the macrostate (N 1 , N 2 ,…N n ) is (13.13) )]. ln( ) ( ln ln [ )! ln( ! ln ! ln ln 1 1 1 1 i i i i i i n i i i n i i i n i i n i i FD N g N g N N g g N g N g − − − − ≈ − − − = ∑ ∑ ∑ ∑ = = = = ω ∑ ∑ = = = = n i i i n i i U N N N 1 1 , , ε With applying the Lagrange multiplier method, we get the maximum ln ω FD corresponding to the equation: j=1, 2,…n (13.15)(13....
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Chapter 13 (II) - 13.2 Fermi-Dirac Statistics j j j j j N g...

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