本课程分五章内容。第一章介绍量子力学发展历史，主要包括十九世纪末物理学与数学发展状态，重要物理实验结果及其中的问题，以及 Planck“量子”概念的提出原因和结果，旧量子论的提出背景、解决的问题和遗留问题，量子力学动力学方程的提出、量子力学理论体系的建立，以及量子力学理论的发展、数学基础、应用和争论。第二章全面回顾总结了以经典力学与经典电动力学为代表的经典物理学基础知识，主要包括 Newton 力学、Lagrange 力学、Hamilton 力学、Helmholtz 矢量分解定理、Maxwell 方程的性质与电磁场的多级展开等，并介绍量子力学数学基础、公理化体系与主要力学量算符，为后续学习打下基础。第三章介绍量子力学中的力学量算符与本征值问题，包括位置和动量、轨道角动量以及自旋角动量，并介绍角动量耦合理论、角动量本征值问题的代数解法、广义不确定性原理（含 Heisenberg 不确定性原理和时间-能量不确定性关系的意义及其与力学量不确定性关系的差别）、力学量的守恒以及对称性变换与守恒量等。第四章介绍定态 Schrödinger 方程，主要包括一维能量本征值基本问题、一维线性谐振子问题、中心力场问题、中心势散射问题、定态微扰论方法以及变分法等。第五章介绍电磁场中的带电粒子，主要包括 Pauli 方程、Landé 因子、Zeeman 效应（正常、反常 Zeeman 效应、Paschen-Back 效应）以及氢原子问题等。

英文简介：Quantum Mechanics (A) includes five chapters. Chapter 1 is an outline of the history of Quantum Mechanics, including the development of physics and mathematics at the end of the nineteenth century, some notable experiments and problems existed, the reason and background of proposing the concept of quanta by Max Planck and of old quantum theory, by which the problems solved and unsolved, the quantum dynamical equations (Heisenberg’s- and Schrödinger’s equations), the construction of the theoretical framework of quantum mechanics and its development and mathematical foundations, the applications and debates of quantum mechanical theories. Chapter 2 is a survey of some fundamentals of classical physics and useful mathematics formulations necessary in quantum mechanics, including Newtonian and analytical (Lagrangian and Hamiltonian) mechanics, classical electrodynamics (Helmholtz’s theorem, derivation and properties of Maxwell’s equations and multipole expansion of electromagnetic field), and some useful vector calculus. Chapter 3 introduces some fundamentals of state/operator in quantum mechanics, including the eigenvalue/eigenvector of the observables (position, momentum, and orbital/spin angular momentum), addition of angular momentum, algebraic methods for solving the eigenvalue problems of angular momentum and the generalized uncertainty principle (including its derivation and its special case, i.e., Heisenberg’s uncertainty principle, where the physical distinction of time-energy uncertainty relation is emphasized), the conservation law in quantum mechanics and some preliminaries of symmetry-conservation relations. Chapter 4 introduces the stationary Schrödinger equation (eigenvalue problems of Hamiltonian), including the one-dimensional potential well/barrier problems, harmonic oscillator problems, central potential and related scattering problems, and time-independent perturbation theory and variational theory. Chapter 5 introduces some fundamental theories to study the interaction of charged particles with electromagnetic field, where the orbital/intrinsic magnetic moment and its interaction with the magnetic field, Pauli equation, Landé g-factor, Zeeman effect (normal and anomalous Zeeman effect and Paschen-Back effect) and the fine/hyperfine structure of hydrogen atom will be mentioned.