Physics: In the FQHE, electrons in a 2D plane under strong B-field form incompressible quantum liquids at fractional filling ν = p/q.
Jain's composite fermion picture: each electron captures q flux quanta, creating a composite particle that sees a reduced effective field B* = B − 2pΦ₀n.
The FQHE at ν = p/(2p±1) maps to the IQHE of composite fermions at integer filling ν* = p.
The Laughlin wavefunction Ψ = ∏ᵢ<ⱼ(zᵢ−zⱼ)ᵐ exp(−Σ|zᵢ|²/4ℓ²) gives the exact ground state for ν=1/m.