Evgeni Korotyaev and Alexander Pushnitski
Trace formulae and high energy asymptotics for the perturbed three-dimensional Stark operator
(66K, Latex 2e)
ABSTRACT. In $L^2(\R^3)$, we consider the unperturbed Stark operator $H_0$
(i.e., the Schr\"odinger operator with a linear potential)
and its perturbation $H=H_0+V$ by an infinitely smooth
compactly supported potential $V$.
The large energy asymptotic expansion for the modified
perturbation determinant for the pair $(H_0,H)$ is obtained
and explicit formulae for the coefficients in this expansion are given.
By a standard procedure, this expansion yields trace formulae
of the Buslaev--Faddeev type.