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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机译：基于阶数的映射方法，最近已经证明了其收敛性，可用于非谐振荡器的能量本征值，可用于求和氢原子斯塔克效应的标准扰动级数。我们进行了一个数值实验，直到摄动展开的第五十级。解析结构和强电场行为所建议的简单映射，与中间值0.03 \ leq E \ leq0.25的电场的精确值非常吻合。能量的虚部（衰减宽度）以及能量的实部是从标准扰动序列中再现的。
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