  In this paper we suggest a simple mathematical procedure to derive the
classical probability density of quantum systems via Bohr's correspondence
principle. Using Fourier expansions for the classical and quantum
distributions, we assume that the Fourier coefficients coincide for the case of
large quantum numbers $n$. We illustrate the procedure by analyzing the
classical limit for the quantum harmonic oscillator, although the method is
quite general. We find, in an analytical fashion, the classical distribution
arising from the quantum one as the zeroth order term in an expansion in powers
of Planck's constant. We interpret the correction terms as residual quantum
effects at the microscopic-macroscopic boundary.
