## Latest post

Aug 30, 2024, 01:11:50

It is wild. I have long been having only 7 agents on my #Huginn instance, and this number increased to 67 in one day. Actually most of them are quite a duplicate of each other, but Huginn has no "template" function or alike.

## 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.

• ### 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.

• ### 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.

• ### 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?

• ### 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 $\varphi(m)\le2$.

• ### 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!

• ### 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.