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