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Mathematical Rigor

Detailed derivations using LaTeX.

Physics Simulations

Interactive demos alongside theory.

Clean Design

Distraction-free reading experience.

Recent Notes & Projects (AI Summarized)

Interferometer Noise and Quantum Noise

Overview of noise sources in Advanced LIGO, focusing on quantum noise and thermal noise.

quantum noisethermal noisegravitational wave detector

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Bose-Einstein Condensation in 2D and 3D

Proves no BEC in 2D ideal Bose gas; derives critical temperature for 3D harmonic trap.

Bose-Einstein condensationideal Bose gasharmonic trap

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QFT: Renormalization and Photon Field

Quantum field theory basics: renormalization, perturbation theory, and photon field quantization.

quantum field theoryrenormalizationphoton field

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Quantum Mechanics Homework 6: Central Force Field

Derivation of kinetic operator and bound state condition in spherical well.

central forcekinetic operatorspherical well

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Quantum Mechanics Homework 7

Seventh assignment covering key quantum mechanics concepts.

quantum mechanicshomeworkphysics

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Feynman Diagrams for Beginners

Introduction to Feynman diagrams and QED calculations with exercises and examples.

Feynman diagramsquantum field theoryQED

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Statistical Mechanics Homework 3: Phase Transition

Derives molar internal energy change and latent heat variation with temperature.

phase transitionClapeyron equationlatent heat

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统计力学第6次作业分析

二维气体速度分布与相对速率分布推导

统计力学速度分布相对速率

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Massless Amplitudes and Spinor-Helicity

Explore 3-point amplitudes for massless particles using spinor-helicity formalism.

massless amplitudesspinor-helicitybootstrap program

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Lecture 6: Chasse_neige & Four Particle Test

Analyzing 4-point amplitudes from 3-point consistency, DoF counting, and Yang-Mills theory.

amplitudesYang-Millson-shell

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引力波的产生、传播与探测

在线性引力近似下分析引力波的产生、传播和探测机制。

引力波线性引力爱因斯坦方程

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统计力学第7次作业分析

求解爱因斯坦固体熵与顺磁固体磁化强度及磁化率。

统计力学配分函数磁化率

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Dyson Series and On-Shell Factorization

Derivation of Dyson series for transition amplitude with source, and on-shell factorization theorem steps.

Dyson seriestransition amplitudeon-shell factorization

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Spinor Helicity for Massless Amplitudes

Introduces spinor helicity formalism to construct massless amplitudes using Lorentz group decomposition.

spinor helicitymassless amplitudesLorentz group

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量子力学作业：阶跃势场反射与透射

求解阶跃势场反射系数R和透射系数T，验证R+T=1，并证明概率守恒。

量子力学阶跃势反射系数

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量子力学中的对称性与守恒量

证明自由粒子角动量守恒及Feynman-Hellmann定理。

角动量守恒Feynman-Hellmann定理量子力学

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On-Shell Factorization in QFT

Analyzes Green functions and pole behavior in scalar field theory.

on-shell factorizationGreen functionscalar field

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Killing Vectors in Schwarzschild Metric

Proving δ^μ_t and δ^μ_φ are Killing vectors of Schwarzschild metric.

Killing vectorsSchwarzschild metricgeneral relativity

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General Relativity Homework 5: Metric Analysis

Calculate connection and Ricci tensor for a time-relevant metric.

Christoffel symbolsRicci tensorgeneral relativity

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量子力学作业：算符性质与不确定性关系

证明逆算符的厄米共轭关系及幺正变换条件，推广不确定性关系。

Hermitian operatorunitary transformationuncertainty relation

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统计力学第5次作业分析

计算两种粒子平衡分布，讨论β与温度对应。

统计力学最概然分布热力学第零定律

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Lecture 2: Integrals and Photon Field

Solving a momentum integral, deriving traceless energy-momentum tensor for photon field.

quantum field theoryresidue theoremenergy-momentum tensor

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Lorentz Invariance and Optical Theorem

Proves Lorentz invariance of inner product and derives optical theorem from S-matrix unitarity.

Lorentz invarianceoptical theoremS-matrix

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Scattering Theory Axioms and Fock Space

Fundamental principles restrain interactions; delve into scattering amplitude using analyticity.

scattering theoryFock spaceanalyticity

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统计力学第4次作业：概率分布与粒子分类

归一化概率分布，求边缘概率，判断粒子为玻色子或费米子。

统计力学概率分布玻色子费米子

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Advanced Calculus: Taylor's Theorem Review

Covers Taylor's theorem with Peano, Lagrange, and Cauchy remainder forms.

Taylor's TheoremRemainder FormsAdvanced Calculus

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Advanced Calculus Homework 1: Series Convergence

Analyzes convergence of six series using comparison, ratio, and root tests.

series convergenceratio testcomparison test

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Advanced Calculus Homework 10 Analysis

Surface and line integrals computed with parameterization and Green's theorem.

surface integralline integralparameterization

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Power Series and Function Expansion

Analysis of power series convergence, expansion of arctan, and properties of zeta function.

power seriesTaylor expansionconvergence

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高等微积分作业：度量空间与不等式

证明连续函数空间度量、Cauchy列收敛、柯西-施瓦茨不等式及开集性质。

度量空间Cauchy列柯西-施瓦茨不等式

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