# Generalized fractional Schroedinger equation with space-time fractional derivatives

## Abstract

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.

- Authors:

- 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 (China)
- (China)

- Publication Date:

- OSTI Identifier:
- 20929684

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 48; Journal Issue: 4; Other Information: DOI: 10.1063/1.2716203; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; FOURIER TRANSFORMATION; GREEN FUNCTION; LAPLACE TRANSFORMATION; MATHEMATICAL SOLUTIONS; POTENTIALS; SCHROEDINGER EQUATION; SPACE-TIME

### Citation Formats

```
Wang Shaowei, Xu Mingyu, and Institute of Applied Mathematics, School of Mathematics and System Science, Shandong University, Jinan 250100.
```*Generalized fractional Schroedinger equation with space-time fractional derivatives*. United States: N. p., 2007.
Web. doi:10.1063/1.2716203.

```
Wang Shaowei, Xu Mingyu, & Institute of Applied Mathematics, School of Mathematics and System Science, Shandong University, Jinan 250100.
```*Generalized fractional Schroedinger equation with space-time fractional derivatives*. United States. doi:10.1063/1.2716203.

```
Wang Shaowei, Xu Mingyu, and Institute of Applied Mathematics, School of Mathematics and System Science, Shandong University, Jinan 250100. Sun .
"Generalized fractional Schroedinger equation with space-time fractional derivatives". United States.
doi:10.1063/1.2716203.
```

```
@article{osti_20929684,
```

title = {Generalized fractional Schroedinger equation with space-time fractional derivatives},

author = {Wang Shaowei and Xu Mingyu and Institute of Applied Mathematics, School of Mathematics and System Science, Shandong University, Jinan 250100},

abstractNote = {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.},

doi = {10.1063/1.2716203},

journal = {Journal of Mathematical Physics},

number = 4,

volume = 48,

place = {United States},

year = {Sun Apr 15 00:00:00 EDT 2007},

month = {Sun Apr 15 00:00:00 EDT 2007}

}

DOI: 10.1063/1.2716203

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