Published April 2007
| Version v1
Journal article
Generalized fractional Schroedinger equation with space-time fractional derivatives
Creators
- 1. Institute of Applied Mathematics, School of Mathematics and System Science, Shandong University, Jinan 250100 (China)
- 2. Institute of Applied Mathematics, School of Mathematics and System Science, Shandong University, Jinan 250100 (China) and Department of Mechanics and Engineering Science, Peking University, Beijing 100871 (CN)
Description
In this paper the generalized fractional Schroedinger equation with space and time fractional derivatives is constructed. The equation is solved for free particle and for a square potential well by the method of integral transforms, Fourier transform and Laplace transform, and the solution can be expressed in terms of Mittag-Leffler function. The Green function for free particle is also presented in this paper. Finally, we discuss the relationship between the cases of the generalized fractional Schroedinger equation and the ones in standard quantum
Additional details
Identifiers
- DOI
- 10.1063/1.2716203;
Publishing Information
- Journal Title
- Journal of Mathematical Physics
- Journal Volume
- 48
- Journal Issue
- 4
- Journal Page Range
- p. 043502-043502.10
- ISSN
- 0022-2488
- CODEN
- JMAPAQ
INIS
- Country of Publication
- United States
- Country of Input or Organization
- International Atomic Energy Agency (IAEA)
- INIS RN
- 38088266
- Subject category
- S71: CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS;
- Descriptors DEI
- FOURIER TRANSFORMATION; GREEN FUNCTION; LAPLACE TRANSFORMATION; MATHEMATICAL SOLUTIONS; POTENTIALS; SCHROEDINGER EQUATION; SPACE-TIME
- Descriptors DEC
- DIFFERENTIAL EQUATIONS; EQUATIONS; FUNCTIONS; INTEGRAL TRANSFORMATIONS; PARTIAL DIFFERENTIAL EQUATIONS; TRANSFORMATIONS; WAVE EQUATIONS
Optional Information
- Notes
- (c) 2007 American Institute of Physics