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• Oct 18, 2023

  You can replace $\mathrm i$ with $-\mathrm i$ in the Schrödinger equation?

  When someone asks you why it is $-\mathrm i$ here instead of $\mathrm i$ or the other way around, you can say that this is just a convention. My professor of quantum mechanics once asked the class similar a question, and I replied with this letter.

  • Categories: physics
  • Tags: quantum mechanics, letter, complex
• Sep 29, 2023

  How to self-host Overleaf (ShareLaTeX)

  It has been a pain setting up Overleaf on my own server. I have finally figured it out and I am sharing my notes here.

  • Categories: guide
  • Tags: linux, selfhosting, tex
• Sep 17, 2023

  My old computers and my experience of daily driving Linux and self-hosting

  I have been using Linux and self-hosting for over a year now. Overall, I would like to say that it is rather satisfactory and that I will continue to use Linux as my daily driver in future. Thinking of that, I felt a little bit nostalgic about my old computers. So I decided to write an article about my old computers and my experience of daily driving Linux now.

  • Categories: misc
  • Tags: linux, selfhosting
• Sep 8, 2023

  I created Sunniesnow, a rhythm game similar to Lyrica

  In order to build a better player community for the rhythm game Lyrica, I created a new rhythm game called Sunniesnow. Learn more about Sunniesnow by joining our Discord server.

  • Categories: update
  • Tags: update, rhythm game, web
• May 9, 2023

  The distribution when indistinguishable balls are put into boxes

  Suppose there are $n$ distinguishable boxes and $k$ indistinguishable balls. Now, we randomly put the balls into the boxes. For each of the boxes, what is the probability that it contains $m$ balls? This is a simple combanitorics problem that can be solved by the stars and bars method. It turns out that in the limit $n,k\to\infty$ with $k/n$ fixed, the distribution tends to be a geometric distribution.

  • Categories: math
  • Tags: probability, combinatorics, ruby
• May 7, 2023

  Labeled break, next, and redo in Ruby

  Many languages support breaking out of nested loops, such as Perl, Java, JavaScript, C#, etc. Languages that have goto can also do this easily. However, in most other languages, it is not easy to break out of nested loops. I want to introduce a way to do this in Ruby.

  • Categories: programming
  • Tags: meta programming, ruby
• May 1, 2023

  Free trade (single good case)

  I set up a simple model to determine the production and consumption in free trade between nations.

  • Categories: economics
  • Tags: global economy, from zhihu
• May 1, 2023

  A measure-theoretic formulation of statistical ensembles (part 2)

  For sake of rigor and generalizability, I feel it necessary to try to have a mathematical formulation for statistical ensembles. I chose measure spaces as the underlying mathematical structure of thermal systems and tried to justify the method of statistical ensembles by deducing them from some axioms.

  • Categories: physics
  • Tags: mathematical physics, statistical mechanics, functional analysis, measure theory, probability, long paper
• Apr 5, 2023

  Summarizing my methods for studying

  I summarized my methods for studying. This can be served as a guide for those who have started learning math and science.

  • Categories: misc
  • Tags: chinese, school
• Mar 30, 2023

  A measure-theoretic formulation of statistical ensembles (part 1)

  For sake of rigor and generalizability, I feel it necessary to try to have a mathematical formulation for statistical ensembles. I chose measure spaces as the underlying mathematical structure of thermal systems and tried to justify the method of statistical ensembles by deducing them from some axioms.

  • Categories: physics
  • Tags: mathematical physics, statistical mechanics, functional analysis, measure theory, probability, long paper

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