The algebraic approach to operator perturbation method has been applied totwo quantum--mechanical systems ``The Stark Effect in the Harmonic Oscillator''and ``The Generalized Zeeman Effect''. To that end, two realizations of thesuperoperators involved in the formalism have been carried out. The first ofthem has been based on the Heisenberg--Dirac algebra of $\hat{a}^\dagger$,$\hat{a}$, $\hat{1}$ operators, the second one has been based in the angularmomemtum algebra of $\hat{L}_+$, $\hat{L}_-$ and $\hat{L}_0$ operators. Thesuccessful results achieved in predicting the discrete spectra of both systemshave put in evidence the reliability and accuracy of the theory.
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机译：算子摄动法的代数方法已应用于两个量子力学系统``谐振子的斯塔克效应''和``广义塞曼效应''。为此，已经实现了涉及形式主义的超级操作员的两种实现。其中第一个基于$ \ hat {a} ^ \ dagger $，$ \ hat {a} $，$ \ hat {1} $运算符的Heisenberg-Dirac代数，第二个基于$ \ hat {L} _ + $，$ \ hat {L} _- $和$ \ hat {L} _0 $运算符的angularmomemtum代数。预测两个系统的离散光谱所取得的成功结果证明了该理论的可靠性和准确性。
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