Supersymmetric black hole solutions in supergravity exhibit the "attractor phenomenon", as a result of which the near-horizon geometry depends only on the charges carried by the black hole and not the asymptotic values of the moduli. I will describe the radial quantization of spherically symmetric solutions of supergravity, in effect quantizing this attractor flow, and compute the supersymmetric wave function explicitly. I will comment on the relevance of this quantization for the construction of a partition function for black hole micro-states, consistent with duality symmetries.