Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
Question
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Chapter 5, Problem 5.29P

(a)

To determine

The number of different three particle states can be constructed from three distinguishable particles.

(a)

Expert Solution
Check Mark

Answer to Problem 5.29P

The number of different three particle states can be constructed from three distinguishable particles are 27 states.

Explanation of Solution

Each distinguishable particle can have 3 possible states.

Therefore, the total number of states the three particle can have be

3×3×3=27

Conclusion:

Thus, the number of different three particle states can be constructed from three distinguishable particles are 27 states.

(b)

To determine

The number of different three particle states can be constructed from three identical bosons.

(b)

Expert Solution
Check Mark

Answer to Problem 5.29P

The number of different three particle states can be constructed from three identical bosons are 10 states.

Explanation of Solution

If all particles are in same state: aaa,bbb,ccc3.

If two particles are in same state: aab,aac,bba,bbc,cca,ccb6 (symmetrized).

It all three particles are in different states: abc1 (symmetrized).

Therefore, the total number of state the three particles states can be constructed from identical bosons are 3+6+1=10.

Conclusion:

Thus, the number of different three particle states can be constructed from three identical bosons are 10 states.

(c)

To determine

The number of different three particle states can be constructed from three identical fermions.

(c)

Expert Solution
Check Mark

Answer to Problem 5.29P

The number of different three particle states can be constructed from three identical fermions is 1 state.

Explanation of Solution

Fermions must occupy different states.

All three particles are in different states: abc1 (antisymmetrized).

Therefore, the total number of state the three particles states can be constructed from identical fermions is 1.

Conclusion:

Thus, the number of different three particle states can be constructed from three identical fermions is 1 state.

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