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    <title>Leonard</title>
    <link>https://wzdlc1996.github.io/</link>
    <description>Recent content on Leonard</description>
    <generator>Hugo -- gohugo.io</generator>
    <language>zh_Hans</language>
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    <item>
      <title>From RNN to ChatGPT</title>
      <link>https://wzdlc1996.github.io/artic/datascience/rnnchatgpt/</link>
      <pubDate>Sun, 05 Mar 2023 00:00:00 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/artic/datascience/rnnchatgpt/</guid>
      <description>This note roughly introduces the development in natural language processing during the past decades. The RNN, LSTM, attention, and Transformer would be covered. Then, the technologies behind the recent popular ChatGPT will be shared, including GPT-series models, Prompts, and how to train language model fitting human intent</description>
    </item>
    
    <item>
      <title>对一般刚体的定点转动的统计力学分析</title>
      <link>https://wzdlc1996.github.io/artic/elementary/rigidbodystat/</link>
      <pubDate>Fri, 15 Jul 2022 22:00:00 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/artic/elementary/rigidbodystat/</guid>
      <description>在统计力学中, 我们通常会关注正则动量与坐标. 因为由它们确定的相空间体积元在正则变换下不变. 但在我们实际进行计算时, 却并非总是正则动量与坐标的表达最为方便. 一个例子就是刚体力学中, 我们会偏爱使用转动惯量和惯量主轴的方法来讨论问题. 然而作为角动量, 它们彼此之间并不对易, 因而在处理统计力学积分时往往带来困惑: 我们能使用它们作为被积变量吗? 进一步的, 用刚体转动模型理解多原子分子热容时同样会遇到这个问题. 本文旨在对这个问题给出解答: 在讨论不依赖转动构型的力学量时, 使用主轴角动量作为动力学变量是完全可行的. 变量替换的 Jacobian 只是转动构型的函数.</description>
    </item>
    
    <item>
      <title>Introduction to Measurement Based Quantum Computing</title>
      <link>https://wzdlc1996.github.io/artic/physics/measbasedqcomputing/</link>
      <pubDate>Thu, 19 May 2022 22:16:06 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/artic/physics/measbasedqcomputing/</guid>
      <description>In this note, we will generally discuss the basic conceptions of measurement-based quantum computing(MBQC). We focus on the workflow of MBQC and how to transpile a circuit-based model to MBQC. The parallization for quantum computing and other optimizations are not fully covered but the references are offered. Finally, we discuss the development of MBQC in theoretical perspective.</description>
    </item>
    
    <item>
      <title>Prove the Irrationality of Square Root of 2</title>
      <link>https://wzdlc1996.github.io/artic/elementary/irrasqrttwo/</link>
      <pubDate>Sat, 19 Feb 2022 00:21:44 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/artic/elementary/irrasqrttwo/</guid>
      <description>Various methods of proving the irrationality of the square root of integer 2. Including the method by contradiction and the direct way.</description>
    </item>
    
    <item>
      <title>Machine Learning in Quantum Mechanics, Up to 2021</title>
      <link>https://wzdlc1996.github.io/artic/physics/mlinqphy/</link>
      <pubDate>Sun, 12 Dec 2021 22:50:00 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/artic/physics/mlinqphy/</guid>
      <description>In the recent(at 2021) decades, machine learning algorithms have been popular in almost all disciplines of science and even art. People have found out that a huge share of research and production problems can be viewed as instances of basic tasks that could get well solved with the modern powerful hardware and algorithms. In physics, there has been already plenty of applications covering data manipulation and model/theory discovering. However, just like those famous algorithms in the past, machine learning has its own caveats. Researchers should get well understanding about the boundary of algorithms&amp;rsquo; ability. Being a well-trained user instead of package importer would be the new requirements of people in related fields. In this review, we will discuss the success applications of machine learning in quantum physics in recent years and the potential limitation. Then the reader could get a clearer picture on the development of machine learning and quantum physics frontier.</description>
    </item>
    
    <item>
      <title>Time in Quantum Mechanics</title>
      <link>https://wzdlc1996.github.io/artic/physics/timeinqm/</link>
      <pubDate>Sat, 25 Sep 2021 18:00:00 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/artic/physics/timeinqm/</guid>
      <description>Time in quantum mechanics is always left as an parameter in the equation of motion. In the non-relativistic quantum theory we find time in the derivative of wavefunction, while in the relativistic quantum field theory, it is not at the same status of spatial position: we introduce the space-time dependent field operator only for Lorentz covariance for the equation of motion. Whether can we have an intrinsic interpretation of time flow in quantum mechanics was early discussed by Don Page and William Wootters with the purpose to match the energy superselection rule. Though it may not be a correct theory for our world or even &amp;lsquo;close&amp;rsquo; to it, it is worthy to discuss in modern view here as a consistent approach to the time puzzle.</description>
    </item>
    
    <item>
      <title>Numerical Methods for Schrodinger Equation</title>
      <link>https://wzdlc1996.github.io/artic/physics/numschrodinger/</link>
      <pubDate>Thu, 22 Jul 2021 22:50:00 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/artic/physics/numschrodinger/</guid>
      <description>The first problem we meet in the practice about quantum mechanics is to simulate the quantum time evolution on computer. Formally, it is the numerical simulation of the (time-dependent) Schrodinger Equation. In this review, we discuss various numerical method for the Schrodinger equation and quantum time evolution, including their implementation and error analysis. We will only focus on the non-relativistic quantum mechanics, i.e., the number of degree of freedom is finite.</description>
    </item>
    
    <item>
      <title>Quantum Machine Learning: Quantum Algorithms to Classical Data</title>
      <link>https://wzdlc1996.github.io/artic/physics/qmachinelearning/</link>
      <pubDate>Sat, 19 Dec 2020 14:16:00 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/artic/physics/qmachinelearning/</guid>
      <description>Quantum machine learning is the integration of quantum algorithms within machine learning programs. Generally, we have four different approaches for this purpose, by the type of data (quantum state/data or classical data) and type of algorithm or platform (quantum algorithm/computer or classical algorithm/computer). In this report, we focus on an elementary discussion about aspect of the quantum approach to classical data. The more attractive part about quantum approach to quantum data will be left for future posts.</description>
    </item>
    
    <item>
      <title>Go 语言基础</title>
      <link>https://wzdlc1996.github.io/notes/golang/chap02/</link>
      <pubDate>Thu, 26 Nov 2020 23:19:37 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/notes/golang/chap02/</guid>
      <description>Go语言的基础, 包括保留关键字, 内置变量类型, 基本语法和流程控制, 多文件组织等</description>
    </item>
    
    <item>
      <title>Go的安装与环境配置</title>
      <link>https://wzdlc1996.github.io/notes/golang/chap01/</link>
      <pubDate>Sun, 22 Nov 2020 22:04:41 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/notes/golang/chap01/</guid>
      <description>Go语言开发环境的安装和一些中国大陆会遇到的问题的解决方案. 开始学习Go语言来丰富自己的知识和技能!</description>
    </item>
    
    <item>
      <title>Time Travel and Quantum Computation</title>
      <link>https://wzdlc1996.github.io/artic/physics/ctcquantcomputing/</link>
      <pubDate>Sun, 27 Sep 2020 15:54:07 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/artic/physics/ctcquantcomputing/</guid>
      <description>Time travel, as a famous concept in science fiction, fascinates people for a long time. However for physicists, this is not only a beautiful dream, but also a interesting problem to discuss mathematically. In the community, there are generally two directions about time travel: (1) does it exist and (2) if it indeed exists, what can we do. In this report, we discuss the application of time travel mainly in the field of quantum computation</description>
    </item>
    
    <item>
      <title>对漫画柜页面加密的解析和漫画爬虫</title>
      <link>https://wzdlc1996.github.io/artic/other/mangaspider/</link>
      <pubDate>Fri, 22 Nov 2019 19:24:24 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/artic/other/mangaspider/</guid>
      <description>最近在准备可视化课程的大作业, 正好学习一下python爬虫的知识并且实际地练练手. 就选择了漫画柜网站, 顺便也能够爬一点漫画下来到本地看. 这篇文章主要记录了一下对漫画柜网站的分析和js逆向的过程, 因为是拿来给自己看并且面向中文用户的, 所以就用中文来写了. 同时会分享一下用来下载漫画的爬虫代码. Recently during the preparation of the final project of Visualization class, I plan to learn python spider systematically. As a good choice for practice, I analyzed the logic of the website of Manhuagui(manhuagui.com) and write a simple code for download mangas efficiently. This article mainly covers the analyzation and reverses its javascript, which would be like a boring detective store. Because this article is written for Chinese web users, it is in Chinese. Sorry for those users of the English language.</description>
    </item>
    
    <item>
      <title>Manybody: Functional Integral Formalism</title>
      <link>https://wzdlc1996.github.io/notes/qm/manybody3/</link>
      <pubDate>Sun, 07 Apr 2019 17:09:13 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/notes/qm/manybody3/</guid>
      <description>Classnote for the class in PKU: &amp;lsquo;Quantum Theory for Manybody System&amp;rsquo;. This note give a simple review for the path integral in coordinate space, and generalized it from single particle to many body system with the closure relation generated by coherent state. With the path integral formalism one can further understand the Green&amp;rsquo;s function.</description>
    </item>
    
    <item>
      <title>Manybody: Introduction to Green&#39;s Function</title>
      <link>https://wzdlc1996.github.io/notes/qm/manybody2/</link>
      <pubDate>Tue, 19 Mar 2019 18:48:01 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/notes/qm/manybody2/</guid>
      <description>Classnote for the class in PKU: &amp;lsquo;Quantum Theory for Manybody System&amp;rsquo;. This note gives a review for theory of Green&amp;rsquo;s function. Covers the definition of real-time Green&amp;rsquo;s function of the many body theory at temperature is zero, and the thermal Green&amp;rsquo;s function , or temperature Green&amp;rsquo;s function. And discussion how to extract information from Green&amp;rsquo;s function.</description>
    </item>
    
    <item>
      <title>Introduction to Weak Measurements and Weak Values</title>
      <link>https://wzdlc1996.github.io/artic/physics/weakmeasurement/</link>
      <pubDate>Mon, 18 Mar 2019 16:10:47 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/artic/physics/weakmeasurement/</guid>
      <description>An introduction to weak measurement and weak values. Using the simplest model and perturbation theory to analyze a class of weak measurement process and the concept of weak values. This article gives a comparison between weak measurement and the ordinary measurement in quantum mechanics(which is called as strong measurement) and some interesting application of weak values.</description>
    </item>
    
    <item>
      <title>Manybody: Coherent State</title>
      <link>https://wzdlc1996.github.io/notes/qm/manybody1/</link>
      <pubDate>Mon, 25 Feb 2019 12:44:33 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/notes/qm/manybody1/</guid>
      <description>This is the first classnote for the class in PKU: &amp;lsquo;Quantum Theory for Manybody System&amp;rsquo;. This note gives a brief introduction to Grassmann numbers and then define the generic coherent states of Boson and Fermion, and discuss their properties. The coherent state is widely used in the path integral expression for many body system, or the field theory.</description>
    </item>
    
    <item>
      <title>Interacting Field Theory: Scattering Theory</title>
      <link>https://wzdlc1996.github.io/notes/fieldtheory/intftii/</link>
      <pubDate>Sat, 12 Jan 2019 14:14:27 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/notes/fieldtheory/intftii/</guid>
      <description>We will review the scattering theory which has been studied in quantum-mechanics. The main character is the S-matrix and how to compute cross section by it. Then we will introduce the Lehmann-Symanzik-Zimmermann reduction fomula, which will show the connection between time-ordered Green&amp;rsquo;s function and S-matrix in scattering theory. The former can be computed by the Feynman Diagram and Feynman Rule which we have studied in the last section, and the latter is the only thing we can measure in experiments.</description>
    </item>
    
    <item>
      <title>Interacting Field Theory: Time-ordered Green&#39;s Function</title>
      <link>https://wzdlc1996.github.io/notes/fieldtheory/intfti/</link>
      <pubDate>Sun, 30 Dec 2018 15:42:02 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/notes/fieldtheory/intfti/</guid>
      <description>We will introduce the basic Field Theory with interaction considered, which is the main propose of Field Theory actually. We will use the perturbation theory here. And what can we talk is only perturbation-property of Field theory. Our goal is to show the constraint of the form of Lagrangian in Interacting Field Theory. Then we will show the perturbation expansion of the time-ordered Green&amp;rsquo;s function and the corresponding method: Feynman Diagram and Feynman Rules. Green&amp;rsquo;s Function is widely used in field theory, especially in condensed matter theory. But in QFT we just care the connection between it and scattering theory, which will be discussed in next section.</description>
    </item>
    
    <item>
      <title>Quantization of Free Field: Maxwell Field</title>
      <link>https://wzdlc1996.github.io/notes/fieldtheory/qtzfieldiii/</link>
      <pubDate>Wed, 26 Dec 2018 20:11:35 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/notes/fieldtheory/qtzfieldiii/</guid>
      <description>The canonical quantization of vector Field(Maxwell Field). One can find that the usual quantization procedure(directly using of commutation relationship) does not work for it, because of the Gauge Symmetry. We will introduce the Gupta-Bleuler quantization procedure. It clearly keeps the Lorentz covariance but leads to a Hilbert space with negative matric. For free Maxwell field we can separate them totally, so the probability interpretation will not destroyed. Then we will computation of propagator and do some discussion. At last we will discuss the discrete symmetry of Maxwell Field in Quantum Theory</description>
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    <item>
      <title>Introduction to Relativistic Quantum Mechanics</title>
      <link>https://wzdlc1996.github.io/notes/qm/relativisticqm/</link>
      <pubDate>Mon, 24 Dec 2018 12:10:36 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/notes/qm/relativisticqm/</guid>
      <description>The simple introduction to Relativistic Quantum Mechanics. Mainly about the Dirac equation. Gives some basic understanding about the Dirac equation(in Dirac representation). Get to know some basic consequences of Dirac equation: Orbital angular momentum is not conserved, but the total angular momentum; Zeeman coupling term with g factor is 2; Spin-orbit coupling term and Zitterbewegung: Dirac particle cannot be &amp;ldquo;at rest&amp;rdquo; in classical sense. Even with zero momentum and without external potential, it seems to be oscillating.</description>
    </item>
    
    <item>
      <title>Quantization of Free Field: Dirac Field</title>
      <link>https://wzdlc1996.github.io/notes/fieldtheory/qtzfieldii/</link>
      <pubDate>Sun, 23 Dec 2018 16:27:27 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/notes/fieldtheory/qtzfieldii/</guid>
      <description>The canonical quantization of Spinor Field(Dirac Field). One can find that the usual quantization procedure(canonical commutation relationship) does not work for it, because it leads to the Hamiltonian with no lower bound. To quantize it correctly, we need modify it as the anti-commutation relationship, which means that Dirac particles are Fermions. Then we will computation of propagator and do some discussion. At last we will discuss the discrete symmetry of Dirac Field in Quantum Theory</description>
    </item>
    
    <item>
      <title>Quantization of Free Field: Scalar Field</title>
      <link>https://wzdlc1996.github.io/notes/fieldtheory/qtzfieldi/</link>
      <pubDate>Thu, 20 Dec 2018 14:29:47 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/notes/fieldtheory/qtzfieldi/</guid>
      <description>The canonical quantization of Real-valued Scalar Field(Klein Gordon Field). And computation of propagator and discussion, especially the causality property. At last we will discuss the discrete symmetry of Klein Gordon Field in Quantum Theory</description>
    </item>
    
    <item>
      <title>Scattering Theory</title>
      <link>https://wzdlc1996.github.io/notes/qm/scattering/</link>
      <pubDate>Mon, 17 Dec 2018 12:54:43 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/notes/qm/scattering/</guid>
      <description>Quantum theory for scattering of particles. Theory and applications.</description>
    </item>
    
    <item>
      <title>Classical Fields: Maxwell Field</title>
      <link>https://wzdlc1996.github.io/notes/fieldtheory/classicalfieldsiii/</link>
      <pubDate>Tue, 11 Dec 2018 15:21:14 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/notes/fieldtheory/classicalfieldsiii/</guid>
      <description>The classical field theory for vector field, so-called Maxwell Field. Together with the solution of Maxwell equation and some properties of Maxwell field.</description>
    </item>
    
    <item>
      <title>Classical Fields: Dirac Field</title>
      <link>https://wzdlc1996.github.io/notes/fieldtheory/classicalfieldsii/</link>
      <pubDate>Tue, 11 Dec 2018 15:21:12 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/notes/fieldtheory/classicalfieldsii/</guid>
      <description>The classical field theory for Dirac spinor field, so-called Dirac Field. Together with the solution of Dirac equation and some properties of Dirac field.</description>
    </item>
    
    <item>
      <title>Setup an In-Site Search</title>
      <link>https://wzdlc1996.github.io/artic/other/insitesearchhugo/</link>
      <pubDate>Sun, 09 Dec 2018 14:56:40 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/artic/other/insitesearchhugo/</guid>
      <description>How to add a search bar for in site posts in Hugo. We used the Algolia as the solution provider.</description>
    </item>
    
    <item>
      <title>Perturbation Theory</title>
      <link>https://wzdlc1996.github.io/notes/qm/perturbation/</link>
      <pubDate>Mon, 03 Dec 2018 13:24:17 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/notes/qm/perturbation/</guid>
      <description>The perturbation theory for quantum mechanics. This is a useful method on solve some problems which we cannot handle it analytically</description>
    </item>
    
    <item>
      <title>Quantum Zeno Effect</title>
      <link>https://wzdlc1996.github.io/artic/physics/zenoeffect/</link>
      <pubDate>Thu, 22 Nov 2018 19:23:43 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/artic/physics/zenoeffect/</guid>
      <description>The quantum Zeno effect: an unstable particle will never be found to decay if it is continuously observed. The theoretical analysis and the experiment. And a simple introduction for Many worlds interpretation</description>
    </item>
    
    <item>
      <title>Classical Fields: Scalar Field</title>
      <link>https://wzdlc1996.github.io/notes/fieldtheory/classicalfieldsi/</link>
      <pubDate>Sun, 18 Nov 2018 21:49:41 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/notes/fieldtheory/classicalfieldsi/</guid>
      <description>The classical field theory for scalar field, so-called Klein-Gordon Field. Together with the solution of Klein-Gordon equation and some symmetry analysis.</description>
    </item>
    
    <item>
      <title>Bluetooth Audio Issues</title>
      <link>https://wzdlc1996.github.io/artic/other/linux/bluetoothaudio/</link>
      <pubDate>Thu, 15 Nov 2018 13:13:29 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/artic/other/linux/bluetoothaudio/</guid>
      <description>How to manager the Bluetooth earphones. Switch HSV to A2DP for the better performance.</description>
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    <item>
      <title>如何为特定应用指定GTK3主题</title>
      <link>https://wzdlc1996.github.io/artic/other/linux/gtkthemeperapp/</link>
      <pubDate>Thu, 15 Nov 2018 13:13:29 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/artic/other/linux/gtkthemeperapp/</guid>
      <description>这个笔记记录如何为特定应用指定不同于系统主题的GTK3主题. 主要是为了解决在系统是用黑色主题时因为字体颜色为白色导致linuxqq中难以辨别的问题</description>
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    <item>
      <title>Classical Field Theory</title>
      <link>https://wzdlc1996.github.io/notes/fieldtheory/classicalft/</link>
      <pubDate>Wed, 14 Nov 2018 15:20:07 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/notes/fieldtheory/classicalft/</guid>
      <description>The classical field theory. Lagrange &amp;amp; Hamilton Formalism and the Noether Theorem.</description>
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    <item>
      <title>Angular Momentum and Spin</title>
      <link>https://wzdlc1996.github.io/notes/qm/spin/</link>
      <pubDate>Wed, 14 Nov 2018 11:42:20 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/notes/qm/spin/</guid>
      <description>Angular momentum and spin theory in Quantum mechanics. Contain SU(2) and SO(3) basic concepts and their representation theory</description>
    </item>
    
    <item>
      <title>Symmetry in Quantum Mechanics</title>
      <link>https://wzdlc1996.github.io/notes/qm/symmetry/</link>
      <pubDate>Mon, 12 Nov 2018 14:38:46 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/notes/qm/symmetry/</guid>
      <description>The symmetry theory in quantum mechanics. Including some tricks about solve some problems with it.</description>
    </item>
    
    <item>
      <title>Quantum Dynamics</title>
      <link>https://wzdlc1996.github.io/notes/qm/dynamics/</link>
      <pubDate>Mon, 12 Nov 2018 14:15:58 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/notes/qm/dynamics/</guid>
      <description>The dynamics theory of Quantum mechanics. And basic introduction for path-integral formalism.</description>
    </item>
    
    <item>
      <title>Identical Particles</title>
      <link>https://wzdlc1996.github.io/notes/qm/identicalparticles/</link>
      <pubDate>Mon, 12 Nov 2018 13:42:48 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/notes/qm/identicalparticles/</guid>
      <description>Quantum theory for identical particles. Contain Permutation group theory and Second quantization.</description>
    </item>
    
    <item>
      <title>Basic Concepts of Quantum Mechanics</title>
      <link>https://wzdlc1996.github.io/notes/qm/concepts/</link>
      <pubDate>Mon, 12 Nov 2018 11:36:42 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/notes/qm/concepts/</guid>
      <description>Some basic concepts for Quantum Mechanics.</description>
    </item>
    
    <item>
      <title>Preliminary Mathematics</title>
      <link>https://wzdlc1996.github.io/notes/fieldtheory/premath/</link>
      <pubDate>Mon, 05 Nov 2018 15:45:57 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/notes/fieldtheory/premath/</guid>
      <description>The preliminary Mathematical knowledge for Quantum Field Theory. Containing the Minkowski Spacetime, Lorentz Group, and the representation theory of Lorentz Group.</description>
    </item>
    
    <item>
      <title>Dual Graphic Card Configuration for Manjaro Linux</title>
      <link>https://wzdlc1996.github.io/artic/other/linux/nvidiasetting/</link>
      <pubDate>Wed, 31 Oct 2018 14:48:29 +0800</pubDate>
      
      <guid>https://wzdlc1996.github.io/artic/other/linux/nvidiasetting/</guid>
      <description>How to handle the dual graphic card on Manjaro. We only show the configuration for Nvidia card.</description>
    </item>
    
    <item>
      <title></title>
      <link>https://wzdlc1996.github.io/notes/mathmethod/randomvariable/</link>
      <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
      
      <guid>https://wzdlc1996.github.io/notes/mathmethod/randomvariable/</guid>
      <description>Random Variable Introduction to Probability Theory Probability Space [Definition] : A Probability Space is a triplet $(\Omega, \mathcal{F},\mathbb{P})$ of three elements:
$\Omega$ is a set (called Sample Space) . $\mathcal{F}$ is a Sigma Algebra on $\Omega$. $\mathcal{F}$ is a collection of subsets of $\Omega$ and has the following properties: $\Omega, \varnothing \in \mathcal{F}$ $A\in \mathcal{F} \Rightarrow A^c \equiv \Omega \setminus A \in \mathcal{F}$ A sequence of sets ${A_i}{i=1}^{\infty}$ in which $A_i \in \mathcal{F}$, then $\bigcup{j=1}^{\infty} A_j \in \mathcal{F}$ $\mathbb{P}$ is a Probability Measure: $\mathbb{P}: \mathcal{F}\rightarrow [0,1]$ and has the following properties: (Normalization)$\mathbb{P}(\Omega) = 1$ (Countably additive)$A_1,A_2,\cdots \in \mathcal{F} \ , \ A_i\bigcap A_j=\varnothing \Rightarrow \mathbb{P}(\bigcup_{j=1}^{\infty} A_j) = \sum_{j=1}^{\infty} \mathbb{P}(A_j)$ [Definition] : A Measurable (real-valued) Function on a Measurable Space $(\Omega,\mathcal{F})$ is a function $f:\Omega \rightarrow \mathbb{R}$, which has the property:</description>
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