Singular Potentials in Quantum Mechanics and Ambiguity in the Self-Adjoint Hamiltonian
| dc.creator | Fülöp, Tamás | |
| dc.date | 2007-08-07 | |
| dc.date | 2007-11-16 | |
| dc.date.accessioned | 2026-07-07T09:34:45Z | |
| dc.date.available | 2026-07-07T09:34:45Z | |
| dc.description | For a class of singular potentials, including the Coulomb potential (in three and less dimensions) and $V(x) = g/x^2$ with the coefficient $g$ in a certain range ($x$ being a space coordinate in one or more dimensions), the corresponding Schrödinger operator is not automatically self-adjoint on its natural domain. Such operators admit more than one self-adjoint domain, and the spectrum and all physical consequences depend seriously on the self-adjoint version chosen. The article discusses how the self-adjoint domains can be identified in terms of a boundary condition for the asymptotic behaviour of the wave functions around the singularity, and what physical differences emerge for different self-adjoint versions of the Hamiltonian. The paper reviews and interprets known results, with the intention to provide a practical guide for all those interested in how to approach these ambiguous situations. | |
| dc.description | This is a contribution to the Proc. of the 3-rd Microconference "Analytic and Algebraic Methods III"(June 19, 2007, Prague, Czech Republic), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/ | |
| dc.identifier | https://arxiv.org/abs/0708.0866 | |
| dc.identifier | http://arxiv.org/abs/0708.0866 | |
| dc.identifier | SIGMA 3 (2007), 107, 12 pages | |
| dc.identifier | doi:10.3842/SIGMA.2007.107 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159606 | |
| dc.subject | Quantum Physics | |
| dc.title | Singular Potentials in Quantum Mechanics and Ambiguity in the Self-Adjoint Hamiltonian | |
| dc.type | text |