arXiv subjects

Dong Jianping

Publications and source records attributed to Dong Jianping.

3 recordsLinked to original sources

arXiv2013

Fractional Green's function for the time-dependent scattering problem in the Space-time-fractional quantum mechanics

Integral form of the space-time-fractional Schrödinger 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.

math-ph↗

arXiv2013

Scattering problems in the fractional quantum mechanics governed by the 2D space fractional Schrodinger equation

The 2D space-fractional Schrodinger equation in the time-independent and time-dependent cases for the scattering problem in the fractional quantum mechanics is studied. We define and give the mathematical expression of the Green's functions for the two cases. The asymptotic formulas of the Green's functions are also given, and applied to get the approximate wave functions for the fractional quantum scattering problems.

math-ph↗

arXiv2013

Levy path integral approach to the solution of the fractional Schrödinger equation with infinite square well

The solution to the fractional Schrödinger equation with infinite square well is obtained in this paper, by use of the Lévy path integral approach. We obtain the even and odd parity wave functions of this problem, which are in accordance with those given by Laskin in [Chaos 10 (2000), 780--790].

math-ph↗