  Eigenstates of the planar magnetic Laplacian with homogeneous magnetic field
form degenerate energy bands, the Landau levels. We discuss the unitary
correspondence between states in higher Landau levels and those in the lowest
Landau level, where wave functions are holomorphic. We apply this
correspondence to many-body systems, in particular we represent effective
Hamiltonians and particle densities in higher Landau levels by corresponding
quantities in the lowest Landau level.
