On the absolutely continuous spectrum of Stark Hamiltonians

We study the spectral properties of the Schrodinger operator with a constan t electric field perturbed by a bounded potential. It is shown that if the derivative of the potential in the direction of the electric field is small er at infinity than the electric field, then the spectrum of the correspond ing Stark operator is purely absolutely continuous. In one dimension, the a bsolute continuity of the spectrum is implied by just the boundedness of th e derivative of the potential. The sharpness of our criterion for higher di mensions is illustrated by constructing smooth potentials with bounded part ial derivatives for which the corresponding Stark operators have a dense po int spectrum. (C) 2000 American Institute of Physics. [S0022-2488(00)03809- 3].