Electron-phonon interactions and the states of a crystal electron in an external electric field

The effect of the electron-phonon interactions on the states of a single tightly bound electron in a one-dimensional crystal in an external electric field F is discussed with the help of a master equation for the occupation probabilities of electron states. It is found that the occupation probabilities of the Stark ladder states usually do not provide a good description of the state of the system despite the fact that these were eigenstates in the absence of the interactions. A good description is possible in terms of the occupation probabilities of time-dependent band states with k(t) = k_o + eFt/ h {combining short stroke overlay} since these probabilities satisfy a markoffian master equation.