  We calculate the quantum corrections of the thermodynamic quantities of a
system of confined Bosons at finite temperature. Systematically quantum
corrections are written in a series of $\hbar$, which is convergent when $kT$
is much larger than the spacing between energy levels of the system. We apply
this method to calculate analytically the thermodynamic potential of a weakly
interacting Bose-gas confined in 3-d harmonic oscillator potential. For large
number of particles, quantum corrections become small, and contribute to the
finite size corrections to scaling.
