Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/time-fractional-schr-dinger-equation-0WYDKKGr60
References (18)
-
K. Diethelm (2010)
The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type -
H. Emamirad, A. Rougirel (2017)
Solution operators of three time variables for fractional linear problemsMathematical Methods in the Applied Sciences, 40
-
K. Kirsch (2016)
Methods Of Modern Mathematical Physics -
Mark Reed, H. Simon (1972)
Method of Modern Mathematical Physics -
F. Martín-Reyes, P. Stinga, J. Torrea (2015)
Maximum principles, extension problem and inversion for nonlocal one-sided equationsarXiv: Analysis of PDEs
-
H. Emamirad, A. Rougirel (2018)
Time fractional linear problems on L2(Rd)Bulletin Des Sciences Mathematiques, 144
-
H. Kober (1940)
ON FRACTIONAL INTEGRALS AND DERIVATIVESQuarterly Journal of Mathematics, 1
-
K. Schmüdgen (2012)
Discrete Spectra of Self-adjoint Operators -
Hassan Emamirad, Arnaud Rougirel (2018)
Time fractional linear problems on $$L^2(\mathbb{R}^d)$$ L 2 ( R d )Bull. Sci. Math., 144
-
Yuri Luchko (2013)
Fractional Schrödinger equation for a particle moving in a potential wellJournal of Mathematical Physics, 54
-
B. Hall (2013)
Quantum Theory for Mathematicians -
Julia, Montel. (2011)
Vector-valued Laplace Transforms and Cauchy Problems -
M. Venkataraman (1960)
Spectral Theory in Hilbert SpaceJournal of the Indian Mathematical Society, 24
-
K. Schmüdgen (2012)
Unbounded Self-adjoint Operators on Hilbert Space -
N. Laskin (2002)
Fractional Schrödinger equation.Physical review. E, Statistical, nonlinear, and soft matter physics, 66 5 Pt 2
-
S. Samko, A. Kilbas, O. Marichev (1993)
Fractional Integrals and Derivatives: Theory and Applications -
E. Love (1938)
Fractional Integration, and Almost Periodic FunctionsProceedings of The London Mathematical Society
-
M. Naber (2004)
Time fractional Schrödinger equationJournal of Mathematical Physics, 45
- Publisher
- Springer Journals
- Copyright
- Copyright © Springer Nature Switzerland AG 2019
- Subject
- Mathematics; Analysis
- ISSN
- 1424-3199
- eISSN
- 1424-3202
- DOI
- 10.1007/s00028-019-00525-5
- Publisher site
- See Article on Publisher Site
Abstract
We propose a time-fractional extension of the Schrödinger equation that keeps the main mechanical and quantum properties of the classical Schrödinger equation. This extension is shown to be equivalent to another well identified time first-order PDE with fractional Hamiltonian.
Journal
Journal of Evolution Equations – Springer Journals
Published: Mar 5, 2020