有限差分法解薛定谔方程及其应用

Finite Difference Method for Solving the Schrodinger Equation and Its Application

用有限差分法解薛定谔方程将连续的量子力学本征值问题转化为离散的本征值问题,在Matlab编程环境下易于实现。文章以一维无限深势阱问题检验有限差分法解薛定谔方程,以有势垒的一维无限深势阱问题探究势垒的围栏效应。模拟研究清洁铜表面48个铁原子构成的圆形量子围栏电子态密度,观察到量子围栏对电子态的吸收效应。

The continuous eigenvalue problem of quantum mechanics can be converted into the discrete eigenvalue problem by using finite difference method,and it is very easy to achieve a target by Matlab software. In this paper,the finite difference method for solving the schrdinger equation can be tested with the problem of one dimensional infinite deep potential well,and the fence effect of potential barrier will be explored by one dimensional infinite deep potential well with potential barrier. The density of electronic states of circular quantum corral which is composed of 48 Fe adatoms positioned into a circular ring on the clean Cu surface is simulated and studied,and the sink effect of electronic states under the action of quantum corral is observed.