  Using the method of locally equilibrium statistical operator we consider the
thermalized relativistic quantum fields in an oscillatory trap. We compare this
thermal picture of the confined boson gas with non-relativistic model of
independent factorized sources. We find that they are equivalent in the limit
of very large effective sizes $R$, more exactly, when the Compton wave length
$1/m$ and thermal wave length $1/\sqrt{% mT}$ are much smaller than {\}$R$ .
Under this conditions we study the influence of Bose condensation in finite
volumes on the structure of the Wigner function, momentum spectra and
correlation function.
