格物致知
——《礼记·大学》
统计物理、量子力学与数学基础的讲义和笔记
已完成整理中草稿
Statistical Physics
统计物理
系综、配分函数、量子统计、相变与非平衡 · 42 篇
第一部分 · 预备知识第 1 章、P1–P5
01热力学要点回顾A Review of Thermodynamics讲义P1经典力学要点Essentials of Classical Mechanics讲义P2量子力学要点Essentials of Quantum Mechanics讲义P3电磁学与物质的电、磁性质要点Electromagnetism and the Electric & Magnetic Properties of Matter讲义P4相平衡与相变的热力学Thermodynamics of Phase Equilibria and Phase Transitions讲义P5输运现象与不可逆过程热力学初步Transport Phenomena and Irreversible Thermodynamics讲义结第二至五部分之间的关联（简明版）How Parts II–V Fit Together (Short Version)讲义第二部分 · 统计热力学第 2–9 章
02统计描述的基础：微观态、宏观态与数学工具Foundations of the Statistical Description: Microstates, Macrostates and Mathematical Tools讲义03微正则系综：熵的统计诠释The Microcanonical Ensemble: The Statistical Meaning of Entropy讲义04正则系综：配分函数The Canonical Ensemble: The Partition Function讲义05近独立粒子系统：玻尔兹曼分布与经典统计Nearly Independent Particles: The Boltzmann Distribution and Classical Statistics讲义06定域系统：两能级系统、顺磁性与固体热容Localized Systems: Two-Level Systems, Paramagnetism and the Heat Capacity of Solids讲义07理想气体的统计热力学：分子配分函数与化学平衡Statistical Thermodynamics of Ideal Gases: Molecular Partition Functions and Chemical Equilibrium讲义08巨正则系综The Grand Canonical Ensemble讲义09统计热力学解决了哪些问题What Statistical Thermodynamics Explained讲义结第二部分小结与展望Part II: Summary and Outlook讲义第三部分 · 量子统计第 10–16 章
10固体物理基础（一）：晶体结构与晶格振动Solid-State Basics I: Crystal Structure and Lattice Vibrations讲义11固体物理基础（二）：晶体中的电子Solid-State Basics II: Electrons in Crystals讲义12全同粒子与量子统计分布Identical Particles and the Quantum Distributions讲义13理想费米气体The Ideal Fermi Gas讲义14理想玻色气体与玻色–爱因斯坦凝聚The Ideal Bose Gas and Bose–Einstein Condensation讲义15光子气体与声子气体Photon and Phonon Gases讲义16量子统计解决了哪些问题What Quantum Statistics Explained讲义第四部分 · 相互作用系统与相变第 17–21 章
17实际气体：位力展开与范德瓦尔斯方程Real Gases: The Virial Expansion and the van der Waals Equation讲义18伊辛模型与平均场理论The Ising Model and Mean-Field Theory讲义19朗道相变理论与临界现象Landau Theory of Phase Transitions and Critical Phenomena讲义20重整化群初步（选讲）A First Look at the Renormalization Group (Optional)讲义21相变理论解决了哪些问题What the Theory of Phase Transitions Explained讲义第五部分 · 涨落与非平衡统计物理第 22–26 章
22涨落理论Theory of Fluctuations讲义23布朗运动：朗之万方程与福克–普朗克方程Brownian Motion: The Langevin and Fokker–Planck Equations讲义24线性响应与涨落–耗散定理Linear Response and the Fluctuation–Dissipation Theorem讲义25玻尔兹曼输运方程与 H 定理The Boltzmann Transport Equation and the H-Theorem讲义26非平衡统计物理解决了哪些问题What Non-Equilibrium Statistical Physics Explained讲义第六部分 · 选讲专题与总结第 27–33 章
27历史专题（一）：统计热力学是怎样建立起来的History I: How Statistical Thermodynamics Was Built讲义28历史专题（二）：量子统计的建立History II: The Making of Quantum Statistics讲义29历史专题（三）：相变与非平衡理论的发展History III: Phase Transitions and Non-Equilibrium Theory讲义30随机行走与高分子链统计Random Walks and the Statistics of Polymer Chains讲义31成核与生长的统计理论Statistical Theory of Nucleation and Growth讲义32计算统计物理：蒙特卡罗方法与分子动力学Computational Statistical Physics: Monte Carlo and Molecular Dynamics讲义33总结：各部分的关联、理论的现状与前沿Summary: Connections, Current Status and Frontiers讲义没有匹配的条目
Quantum Mechanics
量子力学
算符、角动量、微扰与混合态 · 0 篇
还没有笔记
Mathematical Methods
数学基础
物理里反复用到的微积分、线性代数与概率 · 29 篇
附录 · 数学要点统计物理讲义
引使用说明与索引How to Use the Appendix, with an Index速查附录 A · 微积分要点A1–A15
A1多元函数、偏导数与链式法则Multivariable Functions, Partial Derivatives and the Chain Rule速查A2全微分、恰当微分与混合偏导数相等Total and Exact Differentials; Equality of Mixed Partials速查A3泰勒展开（一元与多元）Taylor Expansion in One and Several Variables速查A4偏导数恒等式：倒数关系、循环关系、换固定变量Partial-Derivative Identities: Reciprocal, Cyclic, and Changing the Fixed Variable速查A5勒让德变换The Legendre Transform速查A6重积分与变量替换（极坐标、球坐标、雅可比行列式）Multiple Integrals and Change of Variables速查A7含参变量积分：积分号下求导Integrals with a Parameter: Differentiating under the Integral Sign速查A8条件极值与拉格朗日乘子法Constrained Extrema and Lagrange Multipliers速查A9齐次函数与欧拉定理Homogeneous Functions and Euler's Theorem速查A10级数：几何级数、指数与对数展开、用积分近似求和Series: Geometric, Exponential and Logarithmic; Sums as Integrals速查A11矢量分析：梯度、散度、旋度与连续性方程Vector Calculus: Gradient, Divergence, Curl and the Continuity Equation速查A12变分法初步Introduction to the Calculus of Variations速查A13复数、复指数与常系数线性常微分方程Complex Numbers, Complex Exponentials and Linear ODEs with Constant Coefficients速查A14傅里叶级数、傅里叶变换与 δ 函数Fourier Series, Fourier Transforms and the δ Function速查A15偏微分方程初步（扩散方程、波动方程）Introduction to PDEs: The Diffusion and Wave Equations速查附录 B · 线性代数要点B1–B4
B1向量、内积与二次型Vectors, Inner Products and Quadratic Forms速查B2实对称矩阵的正交对角化Orthogonal Diagonalization of Real Symmetric Matrices速查B3行列式与线性变换的体积因子Determinants and the Volume Factor of Linear Maps速查B4复向量空间、厄米算符与狄拉克记号Complex Vector Spaces, Hermitian Operators and Dirac Notation速查附录 C · 概率与统计要点C1–C9
C1随机变量与概率分布（离散与连续）Random Variables and Probability Distributions速查C2期望、方差与矩；詹森不等式Expectation, Variance and Moments; Jensen's Inequality速查C3联合分布、边缘分布与独立性Joint and Marginal Distributions; Independence速查C4排列组合与二项分布Combinatorics and the Binomial Distribution速查C5高斯（正态）分布The Gaussian (Normal) Distribution速查C6大数定律与中心极限定理The Law of Large Numbers and the Central Limit Theorem速查C7随机变量的变换（概率密度的变换）Transformations of Random Variables速查C8泊松分布The Poisson Distribution速查C9随机过程：平稳过程、马尔可夫过程、关联函数与功率谱Stochastic Processes: Stationarity, Markov Processes, Correlation Functions and Power Spectra速查没有匹配的条目