The qaantuin mechanical Coulomb problem in two and three dimensions is solved completely in terms of path integrals. We derive the integral representations for the Green's functions in configuration spnce and recover the wave functions from factorized residues.
The path integral for the propagator is reduced to an ordinary integral in terms of the generators of a canonical transformation, and is evaluated exactly for square potential barriers in one dimension and for the radial square-well potential in two dimensions.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.