PERTURBATIVE RENORMALIZATION IN QUANTUM-MECHANICS

Some quantum mechanical potentials, singular at short distances, lead to ultraviolet divergences when used in perturbation theory. Exactly as in quantum field theory, but much simpler, regularization and renormalization lead to finite physical results, which compare correctly to the ''act ones. The Dirac delta potential, because of its relevance to triviality, and the Aharonov-Bohm potential, because of its relevance to anyons, are used as examples here.