  What quantum states are possible energy eigenstates of a many-body
Hamiltonian? Suppose the Hamiltonian is non-trivial, i.e., not a multiple of
the identity, and L-local, in the sense of containing interaction terms
involving at most L bodies, for some fixed L. We construct quantum states \psi
which are ``far away'' from all the eigenstates E of any non-trivial L-local
Hamiltonian, in the sense that |\psi-E| is greater than some constant lower
bound, independent of the form of the Hamiltonian.
