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Chapter 5: Q33P (page 246)

Suppose you have three particles, and three distinct one-particle stateΨaX,ΨbX,andΨcxare available. How many different three-particle states can be constructed (a) if they are distinguishable particles, (b) if they are identical bosons, (c) if they are identical fermions? (The particles need not be in different states -ΨaX1,ΨaX2Ψax3would be one possibility, if the particles are distinguishable.)

Short Answer

Expert verified

(a)27

(b)10

(c)1

Step by step solution

01

(a)if they are distinguishable

Each particle has 3 possible states: 3 × 3 × 3 = 27.

02

(b) if they are identical bosons

All in same state: aaa, bbb, ccc⇒3.

2 in one state: aab, aac, bba, bbc, cca, ccb⇒6 (each symmetrized).

3 different states: abc (symmetrized)⇒1.

Total: 10.

If they are identical fermions

Only abc (antisymmetrized) ⟹ 1.

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