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.
Author details: | 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 |
Title of parent work (English): | Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics |
Publisher: | Elsevier |
Place of publishing: | Amsterdam |
Publication type: | Article |
Language: | English |
Date of first publication: | 2020/09/10 |
Publication year: | 2020 |
Release date: | 2023/10/16 |
Tag: | Bessel functions; Fox H-function; Green's function; Schrödinger equation; non-integer dimension |
Volume: | 384 |
Issue: | 34 |
Article number: | 126866 |
Number of pages: | 9 |
Funding 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] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
Peer review: | Referiert |