This paper deals with Hamiltonians of the form H = −∇ + v(r), with v(r) periodic along the z direction, v(x, y, z + b) = v(x, y, z). The wavefunctions of H are the well known Bloch functions ψn,λ(r), with the fundamental property ψn,λ(x, y, z + b) = λψn,λ(x, y, z) and ∂zψn,λ(x, y, z + b) = λ∂zψn,λ(x, y, z). We give the generic analytic structure (i.e. the Riemann surface) of ψn,λ(r) and their c...