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Lecture+8

# 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 the system as a whole.

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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? # 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!
: 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
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 1 ways to How many different ways Q can this be achieve?
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Lecture+8 - Quantum Statistical Mechanics Classical...

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