Fractional Green's function for the time-dependent scattering problem in the Space-time-fractional quantum mechanics
Mathematical Physics
2013-02-26 v2 math.MP
Quantum Physics
Abstract
Integral form of the space-time-fractional Schr\"odinger equation for the scattering problem in the fractional quantum mechanics is studied in this paper. We define the fractional Green's function for the space-time fractional Schrodinger equation and express it in terms of Fox's H-function and in a computable series form. The asymptotic formula of the Green's function for large argument is also obtained, and applied to study the fractional quantum scattering problem. We get the approximate scattering wave function with correction of every order.
Cite
@article{arxiv.1301.3206,
title = {Fractional Green's function for the time-dependent scattering problem in the Space-time-fractional quantum mechanics},
author = {Dong Jianping},
journal= {arXiv preprint arXiv:1301.3206},
year = {2013}
}
Comments
9 pages. arXiv admin note: substantial text overlap with arXiv:1301.1006