The algebraic approach to operator perturbation method has been applied to two quantum--mechanical systems ``The Stark Effect in the Harmonic Oscillator'' and ``The Generalized Zeeman Effect''. To that end, two realizations of the superoperators involved in the formalism have been carried out. The first of them 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 angular momemtum algebra of $\hat{ L}_+$, $\hat{ L}_-$ and $\hat{ L}_0$ operators. The successful results achieved in predicting the discrete spectra of both systems have put in evidence the reliability and accuracy of the theory.
Categories: quant-ph