The zero-energy Coulomb problem

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Abstract
A new operator denoted as a zero‐energy Runge–Lenz vector is used to derive a differential equation for the zero‐energy Schrödinger wavefunction in the u representation. An integral equation is also derived in terms of a generalized Fock 4‐vector which, in the zero‐energy limit, yields the correct integral equation for the zero‐energy Green’s function. The zero‐energy aspect of the problem is further exemplified by extracting the zero‐energy results directly from those for negative energies through the taking of the zero‐energy limit, which is construed as making a group contraction from O(4) to E(3).