suppose you have three particles, and three state distinct one particle States,

Question

suppose you have three particles, and three state distinct one particle States, wave function a, wave function B, and wave function C are available. How many three particle States can be constructed,
a. if they are distinguishable particles,
b. if they are identical bosons,
c. if they are identical fermions?

2. Suppose you have three particles, and three state distinct one-particle states a(r), ?1x), and ?(x) are available. How many three-particle states can be constructed a) ifthey are distinguishable particles, b) if they are identical bososns, c) if they are identical fermions? (5 points) (5 points) (5 points)

Explanation / Answer

A. if they are distinguishable particles then we can construct 3! = 6 states ( assuming that no state has more than 2 particles)

they are 1,2,3 ; 1,3,2 ; 2,1,3 ; 2,3,1 ; 3, 1,2 ; 3,2,1

B. if they are fermions we can construct only one state(because they are identical and no state can have 2 or more particles)

C. if they are boson we can arrange as our wish( we can even keep all particles in one state) so number of wars are

all 3 particles occpying same state - we have 3 possiblities

2 particles occpying same state - we have 3C2 possibilies = 3

no 2 particles occpying same state =  we have 1 possiblities

so total number of ways we can construct three particle States for bosans is 3+3+1 = 7

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