530 Physik
Refine
Has Fulltext
- no (1)
Year of publication
- 2020 (1) (remove)
Document Type
- Article (1)
Language
- English (1)
Is part of the Bibliography
- yes (1)
Keywords
- Bessel functions (1)
- Fox H-function (1)
- Green's function (1)
- Schrödinger equation (1)
- non-integer dimension (1)
Institute
- Institut für Physik und Astronomie (1) (remove)
The time-dependent Schrödinger equation in non-integer dimensions for constrained quantum motion
(2020)
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.