The time-dependent Schrödinger equation in non-integer dimensions for constrained quantum motion
- We propose a theoretical model, based on a generalized Schroedinger equation, to study the behavior of a constrained quantum system in non-integer, lower than two-dimensional space. The non-integer dimensional space is formed as a product space X x Y, comprising x-coordinate with a Hausdorff measure of dimension alpha(1) = D -1 (1 < D < 2) and y-coordinate with the Lebesgue measure of dimension of length (alpha(2) = 1). Geometric constraints are set at y = 0. Two different approaches to find the Green's function are employed, both giving the same form in terms of the Fox H-function. For D = 2, the solution for two-dimensional quantum motion on a comb is recovered. (C) 2020 Elsevier B.V. All rights reserved.
| Verfasserangaben: | Irina PetreskaORCiD, Antonio S. M. de Castro, Trifce SandevORCiDGND, Ervin K. Lenzi |
|---|---|
| DOI: | https://doi.org/10.1016/j.physleta.2020.126866 |
| ISSN: | 0375-9601 |
| ISSN: | 1873-2429 |
| Titel des übergeordneten Werks (Englisch): | Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics |
| Verlag: | Elsevier |
| Verlagsort: | Amsterdam |
| Publikationstyp: | Wissenschaftlicher Artikel |
| Sprache: | Englisch |
| Datum der Erstveröffentlichung: | 10.09.2020 |
| Erscheinungsjahr: | 2020 |
| Datum der Freischaltung: | 16.10.2023 |
| Freies Schlagwort / Tag: | Bessel functions; Fox H-function; Green's function; Schrödinger equation; non-integer dimension |
| Band: | 384 |
| Ausgabe: | 34 |
| Aufsatznummer: | 126866 |
| Seitenanzahl: | 9 |
| Fördernde Institution: | bilateral research project, WTZ Mazedonien S&T Macedonia 2018-20 under; the inter-governmental Macedonian-Austrian agreement [MK 07/2018]; Alexander von Humboldt FoundationAlexander von Humboldt Foundation [MKD; 1205769 GF-E]; CNPqConselho Nacional de Desenvolvimento Cientifico e; Tecnologico (CNPQ) [302983/2018-0] |
| Organisationseinheiten: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
| DDC-Klassifikation: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
| Peer Review: | Referiert |
