Page "Identical particles" Paragraph 79
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The indistinguishability of particles has a profound effect on their statistical properties.
To illustrate this, let us consider a system of N distinguishable, non-interacting particles.
Once again, let n < sub > j </ sub > denote the state ( i. e. quantum numbers ) of particle j.
If the particles have the same physical properties, the n < sub > j </ sub >' s run over the same range of values.
Let ε ( n ) denote the energy of a particle in state n. As the particles do not interact, the total energy of the system is the sum of the single-particle energies.
The partition function of the system is
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