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Boundary conditions in quantum mechanics on the discretized half-line.
- Source :
-
Journal of Physics A: Mathematical & Theoretical . Aug2012, Vol. 45 Issue 30, p1-18. 18p. - Publication Year :
- 2012
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 17518113
- Volume :
- 45
- Issue :
- 30
- Database :
- Academic Search Index
- Journal :
- Journal of Physics A: Mathematical & Theoretical
- Publication Type :
- Academic Journal
- Accession number :
- 78178047
- Full Text :
- https://doi.org/10.1088/1751-8113/45/30/305302