  According to the composite fermion theory, the interacting electron system at
filling factor $\nu$ is equivalent to the non-interacting composite fermion
system at $\nu^*=\nu/(1-2m\nu)$, which in turn is related to the
non-interacting electron system at $\nu^*$. We show that several eigenstates of
non-interacting electrons at $\nu^*$ do not have any partners for interacting
electrons at $\nu$, but, upon composite fermion transformation, these states
are eliminated, and the remaining states provide a good description of the
spectrum at $\nu$. We also show that the collective mode branches of
incompressible states are well described as the collective modes of composite
fermions. Our results suggest that, at small wave vectors, there is a single
well defined collective mode for all fractional quantum Hall states.
Implications for the Chern-Simons treatment of composite fermions will be
discussed.
