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Trace formulae and high energy asymptotics for the Stark operator. (English) Zbl 1106.35305

Summary: In \(L^2(\mathbb R^3)\), we consider the unperturbed Stark operator \(H_0\) (i.e., the Schrödinger 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.

MSC:

35J10 Schrödinger operator, Schrödinger equation
47F05 General theory of partial differential operators
47N50 Applications of operator theory in the physical sciences
81Q15 Perturbation theories for operators and differential equations in quantum theory
81U05 \(2\)-body potential quantum scattering theory
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