An approach to nonstandard quantum mechanics
| dc.creator | Raab, Andreas | |
| dc.date | 2006-12-27 | |
| dc.date.accessioned | 2026-07-07T07:37:14Z | |
| dc.date.available | 2026-07-07T07:37:14Z | |
| dc.description | We use nonstandard analysis to formulate quantum mechanics in hyperfinite-dimensional spaces. Self-adjoint operators on hyperfinite-dimensional spaces have complete eigensets, and bound states and continuum states of a Hamiltonian can thus be treated on an equal footing. We show that the formalism extends the standard formulation of quantum mechanics. To this end we develop the Loeb-function calculus in nonstandard hulls. The idea is to perform calculations in a hyperfinite-dimensional space, but to interpret expectation values in the corresponding nonstandard hull. We further apply the framework to non-relativistic quantum scattering theory. For time-dependent scattering theory, we identify the starting time and the finishing time of a scattering experiment, and we obtain a natural separation of time scales on which the preparation process, the interaction process, and the detection process take place. For time-independent scattering theory, we derive rigorously explicit formulas for the Møller wave operators and the S-Matrix. | |
| dc.identifier | https://arxiv.org/abs/math-ph/0612082 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0612082 | |
| dc.identifier | J. Math. Phys. 45 (2004), 4791 | |
| dc.identifier | doi:10.1063/1.1812358 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120703 | |
| dc.subject | Mathematical Physics | |
| dc.title | An approach to nonstandard quantum mechanics | |
| dc.type | text |