Quantum gravity and the Coulomb potential
Quantum gravity and the Coulomb potential
We apply a singularity-resolution technique utilized in loop quantum gravity to the polymer representation of quantum mechanics on $\mathbb{R}$ with the singular $\ensuremath{-}1/|x|$ potential. On an equispaced lattice, the resulting eigenvalue problem is identical to a finite-difference approximation of the Schr\"odinger equation. We find numerically that the antisymmetric sector has …