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- W2015401787 abstract "We consider a 1-particle 3-dimensional Schrödinger operator with Coulomb potential perturbed by a compactly supported functionq(x)(x∈R 3) and by an external electric field. In contrast with the usual treatment of Stark effect, we assume that the electric field is homogeneous only in a bounded region and is zero outside this region. Both the region and the perturbationq(x) are assumed to have a special parabolic symmetry. We give a rigorous derivation of an asymptotic formula for the discrete spectrum of the problem. This formula describes the splitting of the high Rydberg energy levels of an alkali-like atom in an electric field. We give an explicit formula for the «Stark quantum defect» in terms ofq(x) and the strength ℰ of the electric field. We give, also, explicit expressions for zero-order, linear and quadratic terms in the asymptotic expansion of the quantum defect with respect to ℰ → 0. The derivation of the above-mentioned results is nonperturbative. We suggest a method which allows to carry out a very detailed asymptotic analysis of the solutions of the corresponding Schrödinger equation. The main formulas of this work can be used for numerical computations of the quantum defect. This work can, also, be considered as a necessary technical step towards the precise asymptotic analysis of the Stark resonances in the problem without a cut-off of the electrical field potential." @default.
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- W2015401787 date "1995-09-01" @default.
- W2015401787 modified "2023-10-16" @default.
- W2015401787 title "Stark quantum defect for high Rydberg states of three-dimensional Schrödinger operator with screened Coulomb potential" @default.
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- W2015401787 doi "https://doi.org/10.1007/bf02726154" @default.
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