Chapter 5, Problem 5.29P

(a)

To determine

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

Answer to Problem 5.29P

The number of different three particle states can be constructed from three distinguishable particles are $27\text{ states}$.

Explanation of Solution

Each distinguishable particle can have $3$ possible states.

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

$3\times 3\times 3=27$

Conclusion:

Thus, the number of different three particle states can be constructed from three distinguishable particles are $27\text{ states}$.

(b)

To determine

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

Answer to Problem 5.29P

The number of different three particle states can be constructed from three identical bosons are $10\text{ states}$.

Explanation of Solution

If all particles are in same state: $aaa,bbb,ccc\Rightarrow 3$.

If two particles are in same state: $aab,aac,bba,bbc,cca,ccb\Rightarrow 6$ (symmetrized).

It all three particles are in different states: $abc\Rightarrow 1$ (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 $10\text{ states}$.

(c)

To determine

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

Answer to Problem 5.29P

The number of different three particle states can be constructed from three identical fermions is $1\text{ state}$.

Explanation of Solution

Fermions must occupy different states.

All three particles are in different states: $abc\Rightarrow 1$ (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 $1\text{ state}$.