A Numerical Method For Solving Schrodinger Equation Basing On The Meshless Method

During the last two decades, meshless methods have been developed and ef-fectively applied to solve many problems in science and engineering. The meshless methods do not need the grid very much, and it can avoid the grid distorted and twisted problem. It can give expression to particular advantages in some areas, which the finite element method and the boundary method could not solve.The schrodinger equation is an important partial differential equation,it is applied in various fields. In the current work we investigate a different approach to find the solution of the schrodinger equation. This paper presents a numerical scheme to solve the two-dimensional (2D) time-dependent schrodinger equation using the method of particular solutions.We generalize some meshless methods in this article, using the different functions is the major difference in different meshless methods.The layout of the paper is as follows:The first chapter is an introduction. We describe the application back-grounds and the research situations of the meshless methods.In the second chapter, we propose an important meshless method, which is called radial basis function. The radial basis functions play an important part in developing of meshless methods, and it solves a lot of partial differential equation problems.In the third chapter, We describe the application backgrounds and the re-search situations of the method of fundamental solutions. And we give the char-acteristics of this method.In the fourth and fifth chapters, we propose the method of particular so-lutions and some of application of this method. In the fifth chapter, based on the finite difference scheme and radial basis functions, we give a new numerical scheme using one of the meshless method which is called the method of partic-ular solutions for solving two-dimensional time-dependent schrodinger equation. Two numerical examples with good accuracy are given to validate the proposed method.