PERTURBATIONS OF SUPERSYMMETRIC SYSTEMS IN QUANTUM MECHANICS

The methods of supersymmetry are extended to the factorization method. The degeneracy of levels in factorizable systems is broken under perturbations. With the methods of supersymmetry it is possible to state laws on the order of these perturbed energy levels. One proof of a confirmation of these laws has a more algebraic touch and works for first order perturbation theory. The proof of the laws beyond perturbation theory is hard, more of an analytic spirit and exploits convexity properties of the potentials. The convexity properties serve also for an intuitive argument. An important application is the law on the ordering of energy levels in atoms.