Distribution of quantum states in enclosures of finite size: I

We show that the expression for the density of states of a particle in a three-dimensional rectangular box of finite size can be obtained by using directly the Poisson's summation formula instead of using the Walfisz formula or the generalized Euler formula both of which can be derived from the former. We also derive the expression for the density of states in the case of an enclosure in the form of an infinite rectangular slab and apply it to the problem of the Bose-Einstein condensation of a Bose gas of noninteracting particles confined to a thin-film geometry. (author)