The problem of the Zeemann-Stark effect for the hydrogen atom in electromagnetic fields is considered using the irreducible representations of the Karasev-Novikova algebra with quadratic commutation relations. An asymptotics of the series of eigenvalues and the asymptotic eigenfunctions are obtained near the upper boundaries of resonance spectral clusters which are formed near the energy levels of an unperturbed hydrogen atom.

中文翻译：

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谱簇上边界附近的正交电场和磁场中氢原子光谱的渐近性

使用具有二次换向关系的Karasev-Novikova代数的不可约表示来考虑电磁场中氢原子的Zeemann-Stark效应问题。在共振谱簇的上边界附近获得了一系列特征值和渐近本征函数的渐近性，共振谱簇的上边界在不受干扰的氢原子的能级附近形成。