Quantum gravity and the Coulomb potential

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dc.creatorHusain, Viqar
dc.creatorLouko, Jorma
dc.creatorWinkler, Oliver
dc.date2007-07-02
dc.date2007-10-04
dc.date.accessioned2026-07-07T11:17:25Z
dc.date.available2026-07-07T11:17:25Z
dc.descriptionWe 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.
dc.description10 pages, 5 figures. v2: Minor presentational changes. One data point added in Table I
dc.identifierhttps://arxiv.org/abs/0707.0273
dc.identifierhttp://arxiv.org/abs/0707.0273
dc.identifierPhys.Rev.D76:084002,2007
dc.identifierdoi:10.1103/PhysRevD.76.084002
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/193001
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleQuantum gravity and the Coulomb potential
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