Scattering from Singular Potentials in Quantum Mechanics
| dc.creator | Esposito, Giampiero | |
| dc.date | 1998-07-02 | |
| dc.date | 1998-09-30 | |
| dc.date.accessioned | 2026-07-07T10:53:56Z | |
| dc.date.available | 2026-07-07T10:53:56Z | |
| dc.description | In non-relativistic quantum mechanics, singular potentials in problems with spherical symmetry lead to a Schrodinger equation for stationary states with non-Fuchsian singularities both as r tends to zero and as r tends to infinity. In the sixties, an analytic approach was developed for the investigation of scattering from such potentials, with emphasis on the polydromy of the wave function in the r variable. The present paper extends those early results to an arbitrary number of spatial dimensions. The Hill-type equation which leads, in principle, to the evaluation of the polydromy parameter, is obtained from the Hill equation for a two-dimensional problem by means of a simple change of variables. The asymptotic forms of the wave function as r tends to zero and as r tends to infinity are also derived. The Darboux technique of intertwining operators is then applied to obtain an algorithm that makes it possible to solve the Schrodinger equation with a singular potential containing many negative powers of r, if the exact solution with even just one term is already known. | |
| dc.description | 19 pages, plain Tex. In this revised version, the analysis of Eq. (5.29) has been amended, and an appendix has been added for completeness | |
| dc.identifier | https://arxiv.org/abs/hep-th/9807018 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9807018 | |
| dc.identifier | J.Phys.A31:9493-9504,1998 | |
| dc.identifier | doi:10.1088/0305-4470/31/47/010 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/185651 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Scattering from Singular Potentials in Quantum Mechanics | |
| dc.type | text |