Exact results for the thermodynamic properties and mean occupation numbers of a system of noninteracting fermions with equidistant level spacing are presented for an arbitrary number of particles. It is discussed quantitatively how the results converge to the corresponding ones in the grand canonical ensemble when the thermodynamic limit is reached. From the simple calculations it also follows that the thermodynamics of an infinite two-dimensional electron gas is identical to that of a one-dimensional harmonic chain with linearized dispersion. The results generalize and simplify previous approaches to this model published in this journal.

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