Algebraic Formulation of the Operatorial Perturbation Theory. Part 2. Aplications

Abstract

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.