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

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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Talk given by A. Martin at Les Houches, October 2001, to appear in "Few-Body Problems"

Scientific paper

10.1007/s006010200003

We stress that in contradiction with what happens in space dimensions $n \geq 3$, there is no strict bound on the number of bound states with the same structure as the semi-classical estimate for large coupling constant and 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.

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