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 |
|---|---|
| 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 |
