  We present an analysis of Bose-Einstein condensation for a system of
non-interacting spin-0 particles in a harmonic oscillator confining potential
trap. We discuss why a confined system of particles differs both qualitatively
and quantitatively from an identical system which is not confined. One crucial
difference is that a confined system is not characterized by a critical
temperature in the same way as an unconfined system such as the free boson gas.
We present the results of both a numerical and analytic analysis of the problem
of Bose-Einstein condensation in a general anisotropic harmonic oscillator
confining potential.
