Lecture+8 - Quantum Statistical Mechanics Classical...

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Quantum Statistical Mechanics Classical Statistical Mechanics Quantum Mechanics Quantum Statistical Mechanics Using same methods as classical statistic Mechanics taking Quantum properties into account. No longer keep tracking each particles, care more about
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Math's preparation: : 10 different balls, labeled as 1→10. put them in a line, how many different ways to arrange them? ① ② ③ ① ③ ② ④ ② ③ # of ways to choose the 1st ball: 10 # of ways to choose the 2nd ball: 9 # of ways to choose the last ball: 1 Total ways to arrange Q=10! If there are N balls → Q=N!
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: 20 different balls (labeled as 1 to 20), 3 boxes (a, b, c) How many ways to put 5 balls in box a, 5 balls in box b & 10 balls in box c? ( 29 ( 29 ( 29 ( 29 20 20 5 20 5 5 20! (20 5)! box a : box b : box c: ! 5 5 10 5! 20 5 ! 5! 20 5 5 ! Choose 5 balls from 20 Choose another 5 from the rest put all the rest in box c 20! (20 5)! 5! 20 5 ! 5! 20 5 5 ! Q - - - - = = = ÷ ÷ ÷ - - - - = × - - - ( 29 1 2 1 2 3 (20 5 5)! 20! 10! 20 5 10 ! 5!5!10! ! If we have N particles, m boxes, n in box 1,n in box 2 ! ! ! ! m N Q n n n n - - × = - - = L L
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: 20 different balls (1→20), 3 chests, each has 3 drawers 5 balls in chest a, 5 in chest b, 10 in chest c Q=? 5 5 10 each balls in chest a has 3 drawers to choose 20! (3) (3) (3) 5!5!10! b c Q = × × × L L L L differen t states
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Classical Statistical Mechanics basic assumption: in thermal equilibrium, states with same total energy are equally probable. (each way to arrange the balls has same probability to happen) particles are distinguishable 1 2 3 4 1 2 3 4 n 1 2 3 4 1 Consider One particle energy: E E E E E degeneracies: d d d d d Occupation: N N N N N Total # of particle: Total Energy: n n i i N N E = = L L L L L L 1 i i i E N = =
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1 2 3 1
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This note was uploaded on 12/13/2011 for the course PHYS 113B taught by Professor Staff during the Fall '11 term at UC Irvine.

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Lecture+8 - Quantum Statistical Mechanics Classical...

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