Canonical transformations to action and angle variables and their representation in quantum mechanics II. The coulomb problem

Abstract

The ambiguities in the classical canonical transformation leading to action and angle variables of the attractive Coulomb Problem (suitably generalized for positive energies) and the phase space structure they entail are analyzed. The ambiguity group is found to be different for positive and negative energies. Nevertheless it continues to be the essential concept for the construction of the quantum mechanical representation of the classical transformation, which we explicitly obtain.