Stark Hamiltonias ply an exceptional role in then theory of Schrödinger operators since the particular singularity of the electric potential (in one coordinate multiplcation by x extending over the whole space)yields a Schrödinger operator which is not semi-bounded. This needs mathematical methods giffering from the usual treatment, and leads to unusual, sometimes surprising spectral properties(see Sect.8.5). We concentrate in this chapter mainly on representations of the time evolution operator or propagator solving the Schrödinger equation. Thus, our discussion of the Stark effect is far from complete. See, for example, (140, 160, 377, 378) and the references quoted there, for a different approach.
Unable to display preview. Download preview PDF.