Jekyll2026-06-27T16:15:50+08:00https://heliumky.github.io/feed.xmlJerry Chen’s BlogMathematics, Physics, Computer ScienceJerry ChenBooks and Notes2026-06-27T12:00:00+08:002026-06-27T12:00:00+08:00https://heliumky.github.io/2026/06/27/booksThis post summarizes the reference materials stored in the _pdf/ folder. The list is organized by subject and highlights the reading notes and textbooks I use for study, research, and teaching.

Computer Science

Mathematics

Physics

Research Reports

These PDFs are a snapshot of my current study plan: core physics textbooks, computational math references, and programming notes for C++ and machine learning.

If you want, I can also turn this into a book review post with summaries for each title.

]]>Jerry ChenA Simple Finite-Difference Example2026-06-27T12:00:00+08:002026-06-27T12:00:00+08:00https://heliumky.github.io/2026/06/27/finite-difference-exampleThe finite-difference method replaces derivatives with differences between nearby grid points. For example, the second derivative of a function can be approximated by

\[\frac{d^2\psi}{dx^2}\bigg|_{x_i} \approx \frac{\psi_{i+1}-2\psi_i+\psi_{i-1}}{(\Delta x)^2}.\]

This approximation lets us represent the one-dimensional kinetic-energy operator as a matrix:

import numpy as np

n = 100
x = np.linspace(-5.0, 5.0, n)
dx = x[1] - x[0]

diagonal = -2.0 * np.ones(n)
off_diagonal = np.ones(n - 1)

laplacian = (
    np.diag(diagonal)
    + np.diag(off_diagonal, 1)
    + np.diag(off_diagonal, -1)
) / dx**2

From here, we can add a potential-energy matrix and diagonalize the resulting Hamiltonian. This basic construction is the starting point for many numerical quantum-mechanics calculations.

]]>Jerry Chen