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Recently, we have used a projection operator to fix the number of particlesin a second quantization approach in order to deal with the canonical ensemble.Having been applied earlier to handle various problems in nuclear physics thatinvolve fixed particle numbers, the projector formalism was extended to grantaccess as well to quantum-statistical averages in condensed matter physics,such as particle densities and correlation functions. In this light, theoccupation numbers of the subsequent single-particle energy eigenstates are keyquantities to be examined. The goal of this paper is 1) to provide a soundextension of the projector formalism directly addressing the occupation numbersas well as the chemical potential, and 2) to demonstrate how the emergingproblems related to numerical instability for fermions can be resolved toobtain the canonical statistical quantities for both fermions and bosons.

Occupation numbers in a quantum canonical ensemble: a projection operator approach