Generalized fractional Schrödinger equation with space-time fractional derivatives

2007/04/01 by Shaowei Wang, Mingyu Xu · 2 citations
Mathematics · Physics and Astronomy · #Fractional Differential Equations Solutions #Statistical Mechanics and Entropy #Quantum Mechanics and Non-Hermitian Physics

paper · doi:10.1063/1.2716203

Abstract

In this paper the generalized fractional Schrödinger 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 Schrödinger equation and the ones in standard quantum.

Citations

• Some physical applications of fractional Schrödinger equation
• Time fractional Schrödinger equation

Cited by

• Some solutions to the space fractional Schrödinger equation using momentum representation method
• Forward and backward problems for abstract time-fractional Schrödinger equations

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