I'm curious about geometric quantization.

Of course, I know the procedure: Start with a classical phase space $T^{*}X$, $X$ is the configuration space, then do prequantization by creating a prequantum (complex) line bundle (of course, the symplectic structure must satisfy the Bohr-Sommerfeld condition). The space of square integrable sections of this prequantum line bundle is the prequantum Hilbert space, so choose a polarization $P$. The space of all square-integrable sections of the prequantum line bundle that gives zero when we their covariant derivative at any point $x\in T^{*}X$ in the direction of any vector in a Lagrangian subspace modeled by the polarization is the quantum Hilbert space.

My question is as follows:

Why does geometric quantization work?

As I've said, I'm curious about this, so any help would be appreciated.

Cross-posted from: "http://math.stackexchange.com/questions/698297/geometric-quantization".