中文摘要：

为研究和发展薛定谔方程的数值计算方法,本文将有限差分法应用到量子力学求解薛定谔方程本征值问题.在直角坐标系中,对能量本征方程的一般形式进行有限差分解析,并建立相应的差分格式.以一维、二维、三维各向同性谐振子为例,介绍了求解本征值问题差分格式的建立,并进行了编程计算。结果表明有限差分法计算结果相当精确.在量子力学计算和教学中具有广泛的应用前景.

英文摘要：

In order to investigate and develop numerical calculation method for Schrodinger equation, we apply the finite difference method to eigenvalue problems in quantum mechanics. In a Cartesian coordinate system, we carry out a finite difference analysis of a general form of the energy equation. We demonstrate this method in the case of one, two and three-dimensional isotropic harmonic oscillators, the results show that the finite difference method is quite accurate and useful.