Consider a system that has 5 energy states: 2 states at energy , 1 state at ener

Question

Consider a system that has 5 energy states: 2 states at energy , 1 state at energy 0, and 2 states at energy .

(a) (5 points) Write a partition function for the system containing one particle.

(b) (5 points) Write a partition function for the system containing two distinguishable particles.

(c) (5 points) Write a partition function for the system containing two identical bosons.

(d) (5 points) Write a partition function for the system containing two identical fermions.

(e) (10 points) What is the probability of finding the two particles in the same state for the above three cases: distinguishable particles, bosons, and fermions?

Explanation / Answer

(a) (5 points) Write a partition function for the system containing one particle.

1 Energy State

(b) (5 points) Write a partition function for the system containing two distinguishable particles.
5 Energy State

(c) (5 points) Write a partition function for the system containing two identical bosons.

2 Energy State

(d) (5 points) Write a partition function for the system containing two identical fermions.

0 Energy State

(e) (10 points) What is the probability of finding the two particles in the same state for the above three cases: distinguishable particles, bosons, and fermions?

1

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