The Hydrogen Atom in Strong Electric Fields: Summation of the Weak Field Series Expansion

Details The Hydrogen Atom in Strong Electric Fields: Summation of the Weak Field Series Expansion The Hydrogen Atom in Strong Electric Fields: Summation of the Weak Field Series Expansion

1995-12-25

arxiv.org/abs/hep-th/9512197v1

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, 8 figures

Scientific paper

10.1016/0375-9601(96)00243-5

The order dependent mapping method, its convergence has recently been proven for the energy eigenvalue of the anharmonic oscillator, is applied to re-sum the standard perturbation series for Stark effect of the hydrogen atom. We perform a numerical experiment up to the fiftieth order of the perturbation expansion. A simple mapping suggested by the analytic structure and the strong field behavior gives an excellent agreement with the exact value for an intermediate range of the electric field, $0.03\leq E\leq0.25$. The imaginary part of the energy (the decay width) as well as the real part of the energy is reproduced from the standard perturbation series.

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