Energy States and Bloch States for an Accelerated Electron in a Periodic Lattice

The Hamiltonian for an accelerated electron in a periodic one-dimensional lattice is written using normalized coordinates. By this means, the exact functional form for the position and energy dependence of the energy eigenstates is obtained without resorting to the usual approximation methods, such as power-series expansions, perturbation procedures or one-band models. Bloch-type wave functions that fully satisfy Schrödinger's time-dependent equation are obtained by superimposing energy eigenstates using the Stark ladder spacing concept. Such phenomena as Bloch oscillations and Stark ladder effects are then re-examined as a consequence of this new perspective.