TY  - JOUR
A1  - Petreska, Irina
A1  - de Castro, Antonio S. M.
A1  - Sandev, Trifce
A1  - Lenzi, Ervin K.
T1  - The time-dependent Schrödinger equation in non-integer dimensions for constrained quantum motion
JF  - Modern physics letters : A, Particles and fields, gravitation, cosmology, nuclear physics
N2  - 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.
KW  - Schrödinger equation
KW  - non-integer dimension
KW  - Green's function
KW  - Bessel functions
KW  - Fox H-function
Y1  - 2020
U6  - https://doi.org/10.1016/j.physleta.2020.126866
SN  - 0375-9601
SN  - 1873-2429
VL  - 384
IS  - 34
PB  - Elsevier
CY  - Amsterdam
ER  -