  We apply the Chekhov-Eynard-Orantin topological recursion to the curve
corresponding to the quantum harmonic oscillator and demonstrate that the
result is equivalent to the WKB wave function. We also show that using the
multi-differentials obtained by the topological recursion from the harmonic
oscillator curve, one generates naturally the so-called Poincar\'e polynomials
associated with the orbifolds of the metric ribbon graphs.
