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 |
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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 |