The concept of Wannier-Stark ladders, describing the equally spaced spectrum
of a tightly-bound particle in a constant electric field, is generalized to
account for arbitrary slowly-varying potentials. It is shown that an abrupt
transition exists that separates Wannier-Stark-like from effective-mass-like
behavior when the depth of the perturbation becomes equal to the width of the
band of extended states. For potentials bounded from below, the spectrum
bifurcates above the critical energy while the wavefunctions detach from the
effective-mass region and split into two pieces