Generalized fractional Schrodinger equation with space-time fractional derivatives

In this paper the generalized fractional Schrodinger 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 Schrodinger equation and the ones in standard quantum. (c) 2007 American Institute of Physics.