  We take a critical view at the basic definition of extended single particle
states in a non-translationally invariant system. For this, we present the case
of a hierarchical lattice and incorporate long range interactions that are also
distributed in a hierarchical fashion. We show that it is possible to
explicitly construct eigenstates with constant amplitudes (normalized to unity)
at every lattice point for special values of the electron- energy. However, the
end-to-end transmission, corresponding to the above energy of the electron in
such a hierarchical system depends strongly on a special correlation between
the numerical values of the parameters of the Hamiltonian. Keeping the energy
and the distribution of the amplitudes invariant, one can transform the lattice
from conducting to insulating simply by tunning the numerical values of the
long range interaction. The values of these interactions themselves display a
fractal character.
