bosons, fermions, and classical particles

<bosons>

○○○○○○○○○○ (num of balls=10)

UUUUUU      (num of boxes=6)

 

assuming that one can put any number of indistinguishable balls into one box

eg : putting the 3 balls into the first box,

the 3 balls of the rest into the forth one, and put the rest into the last one

⇔　

○○○|||○○○||○○○○

⇔

15C5 = 15C10 = 6H10

in general, if num of balls = r, num of boxes = n, then (n+r-1)C(n-1) = (n+r-1)C(r) = nHr

 

<fermions>

○○○                            (num of balls=3)

UUUUUUUUUU      (num of boxes=10)

assuming that one can put only one ball into one box, what is called, the Pauli exclusion principle ( each ball indistinguishable )

eg : putting the one ball into the first box,

the one of the rest into the ninth one, and the last one into the last one

⇔　

10C3

in general, if num of balls = r, num of boxes = n, then nCr

<classical particles>

 

(1)(2)(3)          (num of balls=3)

UUUUUU      (num of boxes=6)

 

assuming that all balls can go to any one of the six boxes

(each ball identical) all balls can take any one of the boxes.

⇔ repeated permutation, 6^3

in general, if num of balls = r, num of boxes = n, then n^r