  A mechanism to modify the energy band structure is proposed by considering a
chain of periodic scatterers forming a linear lattice around which an external
cylindrical trapping potential is applied along the chain axis. When this
trapping (confining) potential is tight enough, it may modify the bound and
scattering states of the lattice potential, whose three-dimensional nature
around each scattering center is fully taken into account and not resorting to
zero-range pseudo-potentials. Since these states contribute to the formation of
the energy bands, such bands could thereby be continuously tuned by
manipulating the confinement without the need to change the lattice potential.
In particular, such dimensionality reduction by quantum confinement can close
band gaps either at the center or at the edge of the momentum k-space.
