  We propose an ansatz for the wave function of a non-interacting quantum
particle in a deterministic quasicrystalline potential. It is applicable to
both continuous and discrete models and includes Sutherland's hierarchical wave
function as a special case. The ansatz is parameterized by a first cohomology
class of the hull of the structure. The structure of the ansatz and the values
of its parameters are preserved by the time evolution. Numerical results
suggest that the ground states of the standard vertex models on Ammann-Beenker
and Penrose tilings belong to this class of functions. This property remains
valid for the models perturbed within their MLD class, e.g. by adding links
along diagonals of rhombi. The convergence of the numerical simulations in a
finite patch of the tiling critically depends on the boundary conditions, and
can be significantly improved when the choice of the latter respects the
structure of the ansatz.
