Bound States in n Dimensions (Especially n = 1 and n = 2)

摘要

We stress that in contradiction with what happens in space dimensions n ≥ 3, there is no strict bound on the number of bound states with the same structure as the semi-classical estimate for a large coupling constant. We give, in two dimensions, examples of weak potentials with one or infinitely many bound states. We derive bounds for one and two dimensions which have the “right” coupling-constant behaviour for large coupling.