Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 45, Issue 30, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8113/45/30/305302
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Funding
- Natural Sciences and Engineering Research Council of Canada
- STFC (UK)
- National Science Foundation [NSF PHY11-25915]
- STFC [ST/J000388/1] Funding Source: UKRI
- Science and Technology Facilities Council [ST/J000388/1] Funding Source: researchfish
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We investigate nonrelativistic quantum mechanics on the discretized half-line, constructing a one-parameter family of Hamiltonians that are analogous to the Robin family of boundary conditions in continuum half-line quantum mechanics. For classically singular Hamiltonians, the construction provides a singularity avoidance mechanism that has qualitative similarities with singularity avoidance encountered in loop quantum gravity. Applications include the free particle, the attractive Coulomb potential, the scale invariant potential and a black hole described in terms of the Einstein-Rosen wormhole throat. The spectrum is analysed by analytic and numerical techniques. In the continuum limit, the full Robin family of boundary conditions can be recovered via a suitable fine-tuning but the Dirichlet-type boundary condition emerges as generic.
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