Quantum gravity and the Coulomb potential

Details Quantum gravity and the Coulomb potential Quantum gravity and the Coulomb potential

2007-07-02

arxiv.org/abs/0707.0273v2

Phys.Rev.D76:084002,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages, 5 figures. v2: Minor presentational changes. One data point added in Table I

Scientific paper

10.1103/PhysRevD.76.084002

We apply a singularity resolution technique utilized in loop quantum gravity to the polymer representation of quantum mechanics on R with the singular -1/|x| potential. On an equispaced lattice, the resulting eigenvalue problem is identical to a finite difference approximation of the Schrodinger equation. We find numerically that the antisymmetric sector has an energy spectrum that converges to the usual Coulomb spectrum as the lattice spacing is reduced. For the symmetric sector, in contrast, the effect of the lattice spacing is similar to that of a continuum self-adjointness boundary condition at x=0, and its effect on the ground state is significant even if the spacing is much below the Bohr radius. Boundary conditions at the singularity thus have a significant effect on the polymer quantization spectrum even after the singularity has been regularized.

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