  We study the neutral excitations of fractional quantum Hall states in
electronic systems of finite width where an external anisotropy is introduced
by tilting the magnetic field. As in the isotropic case, the neutral collective
excitation can be worked out through the conserving method of composite
fermions in the Hamiltonian theory because the interaction potential has a
natural cutoff due to the quantum well width. We show how such a computation
can be carried out perturbatively for an anisotropic interaction. We find that
unlike the charge gap, the neutral collective gap is much more sensitive to the
tilt and can thus, for certain fractional quantum Hall states, be easily
destroyed by the parallel component of the magnetic field. We also discuss the
convergence of the collective spectrum to the activation gap in the
large-momentum limit.
