## Latest post

After giving some thoughts, I think something like GitHub issues can be the ultimate form of a #socialmedia platform. One can conveniently refer to other issues using just owner/repo and issue number. One can use issue templates. One can use Markdown as well as inserting multimedia contents in comments. One can react with an emoji. These features easily beat Reddit and Mastodon. It only misses normal social platform features like exploration and tagging.

follow me on Mastodon

## Articles

### The smallest wave packet in the lowest Landau level

The smallest wave packet in the lowest Landau level exists, and is a Gaussian wave packet. This turns out to be related to the coherent state of the harmonic oscillator.

- Categories: physics
- Tags: quantum mechanics, condensed matter physics

### Regularizing the partition function of a hydrogen atom

The partition function of a hydrogen atom diverges (only considering bound states). However, we can regularize it to get finite answers. Different regularizations give the same result. They largely agree with the physical arguments for the case of the hydrogen atom at room or cold temperature, but this should be considered a mere coincidence. The results from regularized partition functions cannot generally be trusted.

- Categories: physics
- Tags: statistical mechanics, complex, regularization, long paper

### Letting people know when you are asleep

While you are asleep, indicate that on your Discord and GitHub user status.

### Using nmcli to connect to eduroam in UCSB

Use nmcli to connect to eduroam in UCSB without using the configuration assistant tool provided by eduroam.

### The duality between two plane trajectories related by a conformal map

The conformal map $\fc wz$ transforms the trajectory with energy $-B$ in potential $\fc Uz\ceq A\v{\d w/\d z}^2$ into the trajectory with energy $-A$ in potential $\fc Vw\ceq B\v{\d z/\d w}^2$. I will prove this beautiful result and show some implications of it.

- Categories: physics
- Tags: complex, classical mechanics, canonical transformation, kepler problem, mathematical physics, vector analysis, long paper

### Embed the latest Mastodon post in my website

I show the latest Mastodon post in my website hosted on GitHub Pages, and it does not require JavaScript on the client side. How do I do that?

- Categories: update
- Tags: web, jekyll, selfhosting

### Rotational symmetry of plane lattices as a simple example of algebraic number theory

For a plane lattice, there is only a finite number of different rotational symmetries that are compatible with the discrete translational symmetry. For example, the 5-fold rotational symmetry is not one of them. Why is that? It turns out that whether an $m$-fold symmetry is compatible with translational symmetry is the same as whether $\varphi(m)\le2$.

- Categories: math
- Tags: complex, condensed matter physics, algebraic number theory, lattice, mathematical physics

### I restructured my blog

If you have not noticed, the equations on my blog are now rendered server-side. This change makes it possible for those who turn off JavaScript on their browsers to see the equations. I also updated the theme from Minima v2 to Minima v3.

### An 🎃 easy 👻 but 🍬

*spooky*💀 Ruby challenge“It’s the weekend and you’ve just completed a seance with friends. After communing with the dead, you realize a mysterious message was left behind.” What is the decoded message? Use your Ruby skills to find out!

- Categories: programming
- Tags: ruby, code golf, fooling around

### 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

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