- Nov 13, 2025
The Schrödinger equation is an ODE, so we can approach its solution through Picard iteration. This approach leads to a sum over walks on the graph formed by an orthonormal basis as vertices and the Hamiltonian matrix elements as edge weights. This sum is exactly the Feynman path integral if we choose the position basis and take the continuum limit.
/physics
#ode
#quantum mechanics
#graph theory
#stochastic process
#long paper
- Nov 6, 2025
Nix is a functional programming language primarily used for package management and system configuration. However, it may be interesting to emulate imperative programming constructs within Nix. This post explores how to achieve imperative-style programming in Nix, ipmlementing control flow, exception handling, and interactive IO.
/programming
#nix
#functional programming
- Jul 17, 2025
According to the central limit theorem, the sum of some i.i.d. samples is normally distributed in the limit of large sample size. This fact can be used to implement a multi-pass Gaussian blur filter, where the total number of passes is equal to the number of samples used in the averaging. Through this, we can also see a nice relation to the heat equation, which is not surprising since the heat kernel is a Gaussian function.
/programming
#algorithm
#shader
#probability
#pde
- Jun 22, 2025
There is a gradually-accelerating buildup kickroll at 1:18 in the song Time to beat the odds by 影虎。. In order to know the details of this rhythm, I have to analyze the sample using Python. The main method is to do a short-time Fourier transform and to find the peaks in the high-frequency region of the spectrogram. A linear regression shows that the time intervals decay geometrically.
/music
#fourier transform
#python
- Apr 11, 2025
Several features of the eigenfunctions of the Laplacian on an annulus with homogeneous Neumann boundary condition are discussed. The distribution of the eigenvalues is discussed in detail, making use of a phase angle function called θ. The limiting cases of a disk and a circle are discussed.
/math
#mathematical physics
#pde
#ode
#long paper
- Mar 3, 2025
Indistinguishability plays an important role in enumerative problems in combinatorics. This article explains the concept and significance of particle indistinguishability in statistical mechanics.
/physics
#mathematical physics
#statistical mechanics
#probability
#long paper
#combinatorics
#quantum mechanics
- Jan 9, 2025
It is common for school courses to require students to submit their homework using GitHub. However, this is usually a bad idea for several reasons, potentially including TOS violation, community degradation, and reliability.
/misc
#github
#school