02-14 Evgeni Korotyaev and Alexander Pushnitski

Trace formulae and high energy asymptotics for the perturbed three-dimensional Stark operator (66K, Latex 2e) Jan 9, 02

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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.

Files: 02-14.src( 02-14.keywords , stark8.tex )