Archive of posts in 2023
Even solutions to bound states in an odd number of potential wells
We try solving the even function solutions to the time-independent Schrödinger equation for the potential such that (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 and speed from a far-awar planet. To defend, humans built a field 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
This is what will happen after you get a haircut
Denote the length distribution of one’s hair to be , where is hair length, and is time. Considering that each hair may be lost naturally from time to time (there is a probability of for each hair to be lost within time range from to ) 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.
- Categories: math
- Tags: calculus, probability, 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!
- Categories: language
- Tags: imagination