The stark ladder and other one-dimensional external field problems

For a certain class of analytic potentialsV(x), matrix elements of the resolvent ofH _F = -d ²/dx ² +Fx +V(x) with entire vectors of the translation group have meromorphic continuations from Imz>0 to the whole complex plane. The poles of these continuations are restricted to a discrete set independent of the analytic vectors chosen. Certain random potentials corresponding to an infinite number of particles distributed on the points of a Poisson set lie in this class with probability one as do a large class of periodic potentials.Supported by NSF Grant MCS 78-00101Supported by NSF Grant MCS 79-02490