Trace Formulae and High Energy Asymptotics for the Stark Operator

Abstract

In , we consider the unperturbed Stark operator H0 (i.e., the Schrödinger operator with a linear potential) and its perturbation H = H 0 + Vby 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.