Quantum mechanics of composite fermions

We present a reformulation of the theory of composite fermions based on Read's dipole picture. We show that: (i) Jain's CF wave function can be recast and derived from the dipole picture by interpreting the form as a projection into an incompressible state of vortices, which are introduced as auxiliary degrees of freedom for representing correlated holes; (ii) the state of a composite fermion in external fields is determined by a wave-equation resembling the ordinary Schrödinger equation but with drift velocity corrections, different from that assumed in the Halperin-Lee-Read theory. The reformulated theory can be easily generalized for fractional Chern insulators.