本文采用高斯基展开法与傅里叶变换法，对三维各向同性谐振子势的薛定谔方程进行数值求解．通过高斯基展开法构造基函数系展开波函数，结合变分参数优化方法提高能级计算精度；同时采用傅里叶变换法在动量空间离散化薛定谔方程，并借助快速傅里叶变换算法实现高效数值求解．计算结果与解析解进行了对比，探讨了两种数值方法在求解这一问题时的适用性，评估了各方法在精度、计算效率等方面的表现．本文的研究为量子力学问题的数值计算教学提供了参考．

This study numerically solves the Schrdinger equation for a threedimensional isotropic harmonic oscillator using Gaussian basis expansion and Fourier transform methods. Wave functions are constructed via Gaussian basis functions, with optimization of variational parameters to enhance the accuracy of energy level calculations. Additionally, the Fourier transform method is utilized to discretize the Schrdinger equation in momentum space, employing the fast Fourier transform algorithm to improve computational efficiency. Results are benchmarked against analytical solutions, and the applicability, accuracy, and computational efficiency of both methods are evaluated. This work serves as a reference for numerical computation teaching in quantum mechanics.