Time fractional Schrödinger equation with a limit based fractional derivative

Chuanjin Zu and Xiangyang Yu

Chaos, Solitons & Fractals, 2022, vol. 157, issue C

Abstract: We re-examine the time fractional Schrödinger equation. The effects of different fractional derivatives and different treatments of imaginary unit i on the time fractional Schrödinger equation are studied. Considering the physical meaning of imaginary unit i in the standard Schrödinger equation, we believe that fractional order of imaginary unit i is inappropriate, which is proved by the evolution of a free particle. Meanwhile, comparing with the Caputo fractional derivative with many restrictions, time fractional Schrödinger equation with a limit based fractional derivative is more in line with the existing physical world. Our results might provide a new perspective to understand the time fractional Schrödinger equation.

Keywords: Time fractional Schrödinger equation; Fractional derivative; Imaginary unit (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077922001515
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922001515

DOI: 10.1016/j.chaos.2022.111941

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().