# Ulysses’ trip

## Posts

何为手纸本?

• ### Introducing bra–ket notation to math learners

Bra–ket notation is a good-looking notation! I am sad that it is not generally taught in math courses. Let me introduce it to you.

• ### Even solutions to bound states in an odd number of $\delta$ potential wells

We try solving the even function solutions to the time-independent Schrödinger equation for the potential $V=-\alpha\sum_{j=-n}^n\delta(x-ja)$ such that $E<0$ (bound states).

• ### Defend our earth against aliens’ bullets!

The aliens intiated their attack to the earth! They shoot bullets with mass $m$ and speed $v$ from a far-awar planet. To defend, humans built a field $U=\alpha/r$ that can repel the bullets. What regions are safe? The answer turns out to be the interior of a circular paraboloid.

• ### This is what will happen after you get a haircut

Denote the length distribution of one’s hair to be $f(l,t)$, where $l$ is hair length, and $t$ is time. Considering that each hair may be lost naturally from time to time (there is a probability of $\lambda\,\mathrm dt$ for each hair to be lost within time range from $t$ to $t+\mathrm dt$) and then restart growing from zero length, how will the length distribution of hair evolve with time? It turns out that we may model it with a first-order PDE.

• ### I want to invent a better way to read numbers

Reading numbers in English is a pain. I want to invent a better way to read numbers!

• ### The longest all-$1$ substring of a random bit string

Given your probability of breaking the combo at each note, what is the probability distribution of your max combo in the rhythm game chart? I considered the problem seriously!

• ### I made this, for the number of days in a week is prime

The number of days in a week is prime, so we cannot utilize weekly periods to help us remember periodical events unless the period is a multiple of 7. However, there may be something that we need to get reminded of which happens once per two days or three days. For example, I wash my hair once per two days and wash my clothes once per eight days. To solve the problem, I wrote a Ruby program to help remind me of those routines.

• ### Using ntfy to warn me when my computer is discharging

I use udev and systemd to send a notification to my phone via ntfy automatically whenever my laptop is discharging.

• ### How to construct mechanics in higher dimensions?

We can derive the equation of motion for mechanical systems in a Galileo universe with $\iota$ time dimensions and $\chi$ space dimensions by generalizing the principle of relativity and Hamilton’s principle.