The time-dependent Schrödinger equation in non-integer dimensions for constrained quantum motion
| Autor: | Irina Petreska, Trifce Sandev, Ervin K. Lenzi, Antonio S. M. de Castro |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Physics
Lebesgue measure Mathematical analysis General Physics and Astronomy Fox H-function Space (mathematics) 01 natural sciences 010305 fluids & plasmas Schrödinger equation symbols.namesake Dimension (vector space) Green's function 0103 physical sciences symbols Quantum system Hausdorff measure 010306 general physics |
| Zdroj: | Physics Letters A. 384:126866 |
| ISSN: | 0375-9601 |
| DOI: | 10.1016/j.physleta.2020.126866 |
| Popis: | We propose a theoretical model, based on a generalized Schrodinger 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 × Y , comprising x-coordinate with a Hausdorff measure of dimension α 1 = D − 1 ( 1 D 2 ) and y-coordinate with the Lebesgue measure of dimension of length ( α 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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