## Archive of posts in Feb, 2023

### Relationship between the Gini coefficient and the variance

Both the Gini coefficient and the variance are measures of statistical dispersion. We are then motivated to find the relationship between them. It turns out that there is a neat mathematical relationship between them.

- Categories: economics
- Tags: from zhihu, calculus, probability

### Distinguishing all the letters in handwritten math/physics notes

Personally, I have the demand of handwriting math/physics notes, but an annoying fact about this is that I usually cannot distinguish every letter that may be possibly used well enough. In this article, I will try to settle this problem.

- Categories: misc
- Tags: from zhihu, font, tex, handwriting, long paper

### 手纸本

何为

*手纸本*?- Categories: literature
- Tags: from zhihu, literary composition, short story, chinese

### 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.

- Categories: math
- Tags: from zhihu, quantum mechanics

### 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).

- Categories: physics
- Tags: from zhihu, quantum mechanics

### 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.

- Categories: physics
- Tags: calculus, classical mechanics, kepler problem, from zhihu