Excitation Spectrum of Composite Fermions

We show that the excitation spectrum of interacting electrons at filling factor $\nu=\nu^*/(2\nu^*+1)$ is well described in terms of non-interacting composite fermions at filling factor $\nu^*$, but does not have a one-to-one correspondence with the excitation spectrum of non-interacting electrons at $\nu^*$. In particular, the collective modes of the fractional quantum Hall states are not analogous to those of the integer quantum Hall states. We also speculate on the nature of the compressible state at $\nu=1/2$.