10.1 Setting the Stage
513
Example 10.1 Illustration of differences between FD, BE, MB statistics.
Consider now 2 particles, and 3 states, and ask the question ‘in how many ways
can the 2 particles be arranged in the 3 states using each of Maxwell–Boltzmann,
Fermi–Dirac and Bose–Einstein statistics?’.
Case 1: Maxwell–Boltzmann statistics (distinguishable particles).
State
1
2
3
1, 2 –
–
–
1, 2
–
–
–
1,2
1
2
–
2
1
–
1
–
2
2
–
1
–
1
2
–
2
1
Total number of states = 9
Case 2: Fermi–Dirac statistics (indistinguishable particles).
State
1 2
3
1 1
–
1 –
1
– 1
1
Total number of states = 3
Case 3: Bose–Einstein statistics (indistinguishable particles).
State
1
2
3
1, 1 –
–
–
1, 1
–
–
–
1, 1
1
1
–
1
–
1
–
1
1
Total number of states = 6
Let us now examine the ratio r of the probability that the two particles are found in
the same state to the probability that the two particles are found in different states