 
Summary: Communications in
Commun. math. Phys. 52,239254 (1977) Mathematical
Physics
© by SpringerVerlag1977
Spectral and Scattering Theory ofSchrdinger Operators
Related to the Stark Effect
J. E. Avron* and I. W. Herbst**
Joseph Henry Laboratories of Physics, Princeton University, Princeton, New Jersey 08540, USA
Abstract. We analyze the spectral properties and discuss the scattering theory
of operators of the form H =H0+V> H0=A+Ex. Among our results
are the existence ofwave operators, ±(H,H0), the nonexistence ofbound
states, and a (speculative) description of resonances forcertain classesof
potentials.
I. Introduction
Since 1951, when Kato [10] initiated the mathematical analysis of Schrodinger
operators ofthe form + V(x) [with V{x)>0 asx*oo insome sense] this
class of operators has become quite well understood (see [15,17,18] for references
to original contributions). It isthe purpose of this paper to initiate astudy of the
class ofoperators which result from the above bythe addition ofa potential
corresponding to a constant electric field. We call such operators Stark
