Quantum Mechanics
本课程系统讲授非相对论量子力学的基本原理和方法。内容包括波函数与薛定谔方程、一维定态问题、力学量的算符表示、中心力场、定态微扰论、自旋与角动量耦合、含时微扰与量子跃迁等。课程强调量子力学的数学结构和物理诠释，培养学生运用量子理论解决实际问题的能力，是凝聚态物理、核物理、粒子物理等方向的基础。
This course systematically teaches the basic principles and methods of non-relativistic quantum mechanics. Topics include wave functions and the Schrödinger equation, one-dimensional stationary state problems, operator representation of mechanical quantities, central force fields, stationary state perturbation theory, spin and angular momentum coupling, time-dependent perturbation and quantum transitions. The course emphasizes the mathematical structure and physical interpretation of quantum mechanics, developing students' ability to apply quantum theory to practical problems, serving as the foundation for condensed matter physics, nuclear physics, and particle physics.
使用数值方法求解一维定态薛定谔方程，计算方势阱、谐振子和双势阱等不同势场中的束缚态能级和波函数。要求实现打靶法或有限差分法，计算至少三种不同势场的前几个能级。学生需绘制波函数和概率密度分布图，分析能级随势场参数的变化规律，对于双势阱需研究隧穿效应和能级分裂现象，并与解析结果进行对比。
Solve the one-dimensional stationary Schrödinger equation using numerical methods to calculate bound state energy levels and wave functions in different potentials such as square well, harmonic oscillator, and double well. Required to implement the shooting method or finite difference method, calculating the first few energy levels for at least three different potentials. Students plot wave functions and probability density distributions, analyze how energy levels vary with potential parameters, study tunneling effects and energy level splitting for double wells, and compare with analytical results.